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Adjoints, Transposes and Hermitian Conjugates
 
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The adjoint of an operator on an inner product space is like the transpose, or transpose-conjugate, of a matrix, only more general.
Views: 20611 Lorenzo Sadun
Normal Operators on Real Inner Product Spaces
 
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Normal operators and invariant subspaces. Description of normal operators on real inner product spaces.
Views: 801 Sheldon Axler
Mod-13 Lec-47 Properties of the Adjoint Operation. Inner Product Space Isomorphism
 
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Linear Algebra by Dr. K.C. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in
Views: 4103 nptelhrd
Linear Algebra 25,  Dot Product as a Linear Operator 1 Proof
 
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Linear Algebra 25, Dot Product as a Linear Operator 1 Proof
Views: 470 LadislauFernandes
Self-Adjoint Operators
 
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Self-adjoint operators. All eigenvalues of a self-adjoint operator are real. On a complex vector space, if the inner product of Tv and v is real for every vector v, then T is self-adjoint.
Views: 6232 Sheldon Axler
Isometries on Real Inner Product Spaces
 
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Description of isometries on real inner product spaces as direct sums of the identity operator, the negative of the identity operator, and rotations on subspaces of dimension 2.
Views: 519 Sheldon Axler
Unrolled Memory Inner-Products: An Abstract GPU Operator for Efficient Vision-Related Computations
 
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ICCV17 | 1658 | Unrolled Memory Inner-Products: An Abstract GPU Operator for Efficient Vision-Related Computations Yu Sheng Lin (GIEE, NTU), wei chao Chen (), Shao-Yi Chien (National Taiwan University) Recently, convolutional neural networks (CNNs) have achieved great success in fields such as computer vision, natural language processing, and artificial intelligence. Many of these applications utilize parallel processing in GPUs to achieve higher performance. However, it remains a daunting task to optimize for GPUs, and most researchers have to rely on vendor-provided libraries for such purposes. In this paper, we discuss an operator that can be used to succinctly express computational kernels in CNNs and various scientific and vision applications. This operator, called Unrolled-Memory-Inner-Product (UMI), is a computationally-efficient operator with smaller code token requirement. Since a naive UMI implementation would increase memory requirement through input data unrolling, we propose a method to achieve optimal memory fetch performance in modern GPUs. We demonstrate this operator by converting several popular applications into the UMI representation and achieve 1.3x-26.4x speedup against frameworks such as OpenCV and Caffe.
Linear Algebra 24,  Dot Product as a Linear Operator 1
 
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Linear Algebra 24, Dot Product as a Linear Operator 1
Views: 503 LadislauFernandes
Cobra Operator Belt  + Inner by FROG.PRO [war belt]
 
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Leggero, rigido, minimale, ma soprattutto tenace. Sono molto soddisfatto di questo nuovo prodotto della FROG.PRO; la Cobra Operator Belt può essere adoperata in quasi ogni contesto e può sopportare carichi anche molto elevati. Le prossime recensioni saranno dedicate alle tasche e a come settarla in base ai diversi contesti. #tacticalequipment #frogpro #platecarrier ==================================================== * Puoi trovarlo qua : https://www.frogpro.it/it/prodotto/cobra-operator-belt/ * Iscriviti al canale per seguire gli aggiornamenti * Seguimi anche su Facebook: https://www.facebook.com/93tacco/ * Seguimi su Instagram per le anteprime: https://www.instagram.com/tacco_solution/?hl=it
Views: 1469 Alberto Tacco
Representation Theory 5, Inner Product Space
 
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Representation Theory 5, Inner Product Space
Views: 852 LadislauFernandes
INNER PRODUCT SPACE || INNER PRODUCT SPACES IN LINEAR ALGEBRA
 
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Inner product space in hindi. Inner product vector space with example. Solved example of inner product space in hindi. Inner product space in matrix. Linear Algebra. Inner product space in hindi. Gram-Schmidt Orthogonalization Process - Linear Algebra: https://www.youtube.com/playlist?list=PLtFV0hYqGnEmH5UMu8-I8VXKoCwwiwikn Linear transformation - Linear Transformation - complete concept & fully solved questions in hindi: https://www.youtube.com/playlist?list=PLtFV0hYqGnElZ6QJojALui-zhDrbRiIqs Please subscribe the chanel for more vedios and please support us.
Views: 16791 Mathematics Analysis
Lecture 1 (Part 3): Inner product space and inner product on R^d and c[a,b]
 
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The course intends to give an introduction to functional analysis, which is a branch of analysis in which one develops analysis in infinite dimensional vector spaces. The central concepts which are studied, are normed spaces with emphasis on Banach and Hilbert spaces, and continuous linear maps (often called operators) between such spaces. Spectral theory for compact operators is studied in detail, and applications are given to integral and differential equations.
MATH426: Matrix norms
 
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Views: 43262 Toby Driscoll
\braket{x|p} = ? Inner product of position and momentum eigenstates
 
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Hey How to Basic here to show you what the inner product of these two eigenstates are. plot twist it's not zero in case you thought it be zero.
Views: 3058 Andrew Dotson
Mod-01 Lec-21 Inner Product & Hilbert Space
 
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Functional Analysis by Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
Views: 27794 nptelhrd
Bras and Kets II: Non-standard Inner Products
 
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When working with a non-standard inner product, we have to compute the metric matrix. This changes the form of the bras, but not the kets.
Views: 2212 Lorenzo Sadun
What is an Inner Product Space?
 
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This video covers the definition of an inner product and an inner product space, length, distance and angles in an inner product space, the inner product on the vector space of continuous functions, orthogonality, the Pythagorean Theorem, and an example from communication engineering of the importance of distance in creating good communication codes.
Views: 370 John Harland
Adjoints
 
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Algebraic properties of the adjoint. Null space and range of the adjoint. The matrix of T* is the conjugate transpose of the matrix of T.
Views: 3718 Sheldon Axler
Positive Operators
 
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Positive operators. Square roots of operators. Characterization of positive operators. Each positive operator has a unique positive square root.
Views: 1422 Sheldon Axler
Linear Algebra: Lecture 34: complex inner product space, Hermitian conjugate and properties
 
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Continuing Lecture 33, I fix the proof of coordinate independence of the projection to begin. Then we study complex inner product spaces briefly. Symmetric and self-adjoint linear transformations are discussed. I SHOULD have called self-adjoing linear transformations "Hermitian operators" hence the result that the e-values of a Hermitian operator are real. Finally I sketched the proof of the spectral theorem. I hope I've shown enough for you to understand the proof in Damiano and Little. Next time I'll emphasize a couple points I missed in this Lecture (why complex matters for the existence of an e-value, and the more general topic of allowed coordinate change). Then we begin work on generalized e-vector theory aka Chapter 6 of Damiano and Little.
Views: 1588 James Cook
Introduction to Hermitian and Unitary Matrices
 
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We go over what it means for a matrix to be Hermitian and-or Unitary. We quickly define each concept and go over a few clarifying examples. We will use the information here in the proofs in future videos. NOTE: I need a microphone, badly. I also tried to write some of this presentation out, but it seemed a bit chopped. In the future I will probably freestyle it.
Views: 38470 Ron Joniak
Mod-01 Lec-22 Further Properties of Inner Product Spaces
 
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Functional Analysis by Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
Views: 8388 nptelhrd
Lec09 線性代數(二) 第六章 Inner Product Spaces
 
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6.4 Normal And Self-Adjoint Operators 授課教師:應用數學系 莊重老師 課程資訊:http://ocw.nctu.edu.tw/course_detail.php?bgid=1&gid=1&nid=361 授權條款:Creative Commons BY-NC-SA 更多課程歡迎瀏覽交大開放式課程網站:http://ocw.nctu.edu.tw/ 本課程同時收錄至國立交通大學機構典藏,詳情請見: http://ir.nctu.edu.tw/handle/11536/108205
Views: 3387 NCTU OCW
Using Orthogonal Bases II: Decomposing Operators
 
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We can compute the matrix elements of any operator (relative to an orthonormal basis) using inner products. This video shows how.
Views: 1278 Lorenzo Sadun
Lec08 線性代數(二) 第六章 Inner Product Spaces
 
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6.3 The Adjoint of a Linear Operator 授課教師:應用數學系 莊重老師 課程資訊:http://ocw.nctu.edu.tw/course_detail.php?bgid=1&gid=1&nid=361 授權條款:Creative Commons BY-NC-SA 更多課程歡迎瀏覽交大開放式課程網站:http://ocw.nctu.edu.tw/ 本課程同時收錄至國立交通大學機構典藏,詳情請見: http://ir.nctu.edu.tw/handle/11536/108205
Views: 4971 NCTU OCW
Introduction to Quantum Computing (8) - Inner Product
 
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The inner product is an operation that takes two vectors and produces a number. It satisfies several axioms. A vector is normalized if its inner product with itself is 1. Two vectors are orthogonal if their inner product is 0. Normalized, orthogonal vectors are orthonormal.
Views: 1582 daytonellwanger
Mod-14 Lec-50 Self-Adjoint Operators II - Spectral Theorem
 
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Linear Algebra by Dr. K.C. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in
Views: 4786 nptelhrd
Introduction to projections | Matrix transformations | Linear Algebra | Khan Academy
 
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Determining the projection of a vector on s line Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/expressing-a-projection-on-to-a-line-as-a-matrix-vector-prod?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Missed the previous lesson? https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/unit-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 302175 Khan Academy
Polar Decomposition
 
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The analogy between the complex numbers and L(V). The Polar Decomposition: If T is an operator on a finite-dimensional inner product space V, then there exists an isometry on V such that T equals S times the square root of T*T.
Views: 1324 Sheldon Axler
Inner product and Dirac Notation | Quantum Mechanics | LetThereBeMath |
 
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In this video we continue talking about eigenstates and discuss the inner product and bra-ket notation, more formally known as Dirac notation.
Views: 745 LetThereBeMath
Mod-14 Lec-51 Normal Operators - Spectral Theorem
 
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Linear Algebra by Dr. K.C. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in
Views: 8447 nptelhrd
Tensor Calculus Lecture 12b: Inner Products in Tensor Notation
 
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This course will continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Solutions: http://bit.ly/ITACMS_Sol_Set_YT Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Weyl's masterpiece: http://bit.ly/SpaceTimeMatter Levi-Civita's classic: http://bit.ly/LCTensors Linear Algebra Videos: http://bit.ly/LAonYT Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Tensor Calculus Change of Coordinates The Tensor Description of Euclidean Spaces The Tensor Property Elements of Linear Algebra in Tensor Notation Covariant Differentiation Determinants and the Levi-Civita Symbol The Tensor Description of Embedded Surfaces The Covariant Surface Derivative Curvature Embedded Curves Integration and Gauss’s Theorem The Foundations of the Calculus of Moving Surfaces Extension to Arbitrary Tensors Applications of the Calculus of Moving Surfaces Index: Absolute tensor Affine coordinates Arc length Beltrami operator Bianchi identities Binormal of a curve Cartesian coordinates Christoffel symbol Codazzi equation Contraction theorem Contravaraint metric tensor Contravariant basis Contravariant components Contravariant metric tensor Coordinate basis Covariant basis Covariant derivative Metrinilic property Covariant metric tensor Covariant tensor Curl Curvature normal Curvature tensor Cuvature of a curve Cylindrical axis Cylindrical coordinates Delta systems Differentiation of vector fields Directional derivative Dirichlet boundary condition Divergence Divergence theorem Dummy index Einstein summation convention Einstein tensor Equation of a geodesic Euclidean space Extrinsic curvature tensor First groundform Fluid film equations Frenet formulas Gauss’s theorem Gauss’s Theorema Egregium Gauss–Bonnet theorem Gauss–Codazzi equation Gaussian curvature Genus of a closed surface Geodesic Gradient Index juggling Inner product matrix Intrinsic derivative Invariant Invariant time derivative Jolt of a particle Kronecker symbol Levi-Civita symbol Mean curvature Metric tensor Metrics Minimal surface Normal derivative Normal velocity Orientation of a coordinate system Orientation preserving coordinate change Relative invariant Relative tensor Repeated index Ricci tensor Riemann space Riemann–Christoffel tensor Scalar Scalar curvature Second groundform Shift tensor Stokes’ theorem Surface divergence Surface Laplacian Surge of a particle Tangential coordinate velocity Tensor property Theorema Egregium Third groundform Thomas formula Time evolution of integrals Torsion of a curve Total curvature Variant Vector Parallelism along a curve Permutation symbol Polar coordinates Position vector Principal curvatures Principal normal Quotient theorem Radius vector Rayleigh quotient Rectilinear coordinates Vector curvature normal Vector curvature tensor Velocity of an interface Volume element Voss–Weyl formula Weingarten’s formula Applications: Differenital Geometry, Relativity
Views: 4847 MathTheBeautiful
Bras and Kets I: Standard Inner Products
 
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We write the inner product of two vectors as a bracket. This can be viewed as the product of a "bra" and a "ket". We explain what these mean for standard inner products on R^n and C^n, and work some examples.
Views: 4692 Lorenzo Sadun
[VECTOR SPACES 3] Inner Product
 
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Inner Product, introduction, uses, orthogonal and orthonormal basis, obtaining vector components, and projecting vectors into subspaces. King's College London - Physics Programme - Year 1 Maths Video Lecture CONTENTS: - Vector Basis [0:33] - Intro to Inner Product [0:12] - Uses of Inner Product [1:31] - Orthogonal and orthonormal basis [2:29] - Obtaining vector components [4:50] - Projection of vector into subspace [12:00] - Inner product as generalization of dot product [16:04] - Axioms for inner product [16:37] & [17:20] - Dot product does not work on complex vectors [19:10] - Hermitian inner product [20:55] - Schwarz's and triangle inequalities [24:40] - Calculating inner product in terms of orthonormal basis components [26:25] - Note on different notations [31:00] Francisco (Paco) Rodríguez Fortuño Senior Lecturer King's College London
Views: 366 PakVideoLectures
ece501b_vid8.2_11_07_2016
 
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ECE 501B Video 8.2: Normal Operators and Spectral Theorem on Complex Inner Product Space. Produced by the Electrical and Computer Engineering Department at the University of Arizona.
Views: 37 Hal Tharp
RotationOperatorPt1.wmv
 
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The Rotation Operator on the Euclidean Space E^2 as a Tensor Operator. Using geometric thinking and the "Balance of Information" to derive an explicit formula for the Rotation Tensor. The Matrix Representation, Orthogonal Matrices and the Rotation Group SO_2. The Rotation Group as a Lie Group. Invariance properties of inner products under R(theta).
Views: 2299 Mathview
Complexification
 
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The complexification of a real vector space. The complexification of an operator on a real vector space. Every operator on a nonzero finite-dimensional real vector space has an invariant subspace of dimension 1 or 2. Every operator on an odd-dimensional real vector space has an eigenvalue. The characteristic and minimal polynomials of an operator on a real vector space.
Views: 595 Sheldon Axler
Mathematics of Quantum 2 (Inner Product)
 
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Mathematical Structure of Quantum Mechanics 2 by Kaveh in simple words Inner Product Bra-Ket
Views: 1277 Kaveh Mozafari
DISTANCE IN INNER PRODUCT SPACE 🔥
 
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Distance in inner product space in hindi. Distance in inner product space theorem proof. Distance in inner product space examples. Inner product space. Please subscribe the chanel for more vedios and please support us.
Nilpotent Operators
 
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If N is a nilpotent operator on a finite-dimensional vector space, then there is a basis of the vector space with respect to which N has a matrix with only 0's on and below the diagonal.
Views: 1168 Sheldon Axler
Self adjoint operators over hilbert spaces and its eigen values and eigen vectors.(MATH)
 
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Subject:-Mathematics Paper:- Functional Analysis Principal Investigator:-Prof.M. Majumdar
Views: 1920 Vidya-mitra
Mod-14 Lec-48 Unitary Operators
 
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Linear Algebra by Dr. K.C. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in
Views: 4881 nptelhrd
Mathematics of Quantum 15 (Operators, Identity , Other Product)
 
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Mathematical Structure of Quantum Mechanics 15 By Kaveh Operators Identity Other Product
Views: 517 Kaveh Mozafari
Tensor Calculus 4e: Decomposition by Dot Product in Tensor Notation
 
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This course will continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Solutions: http://bit.ly/ITACMS_Sol_Set_YT Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Weyl's masterpiece: http://bit.ly/SpaceTimeMatter Levi-Civita's classic: http://bit.ly/LCTensors Linear Algebra Videos: http://bit.ly/LAonYT Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Tensor Calculus Change of Coordinates The Tensor Description of Euclidean Spaces The Tensor Property Elements of Linear Algebra in Tensor Notation Covariant Differentiation Determinants and the Levi-Civita Symbol The Tensor Description of Embedded Surfaces The Covariant Surface Derivative Curvature Embedded Curves Integration and Gauss’s Theorem The Foundations of the Calculus of Moving Surfaces Extension to Arbitrary Tensors Applications of the Calculus of Moving Surfaces Index: Absolute tensor Affine coordinates Arc length Beltrami operator Bianchi identities Binormal of a curve Cartesian coordinates Christoffel symbol Codazzi equation Contraction theorem Contravaraint metric tensor Contravariant basis Contravariant components Contravariant metric tensor Coordinate basis Covariant basis Covariant derivative Metrinilic property Covariant metric tensor Covariant tensor Curl Curvature normal Curvature tensor Cuvature of a curve Cylindrical axis Cylindrical coordinates Delta systems Differentiation of vector fields Directional derivative Dirichlet boundary condition Divergence Divergence theorem Dummy index Einstein summation convention Einstein tensor Equation of a geodesic Euclidean space Extrinsic curvature tensor First groundform Fluid film equations Frenet formulas Gauss’s theorem Gauss’s Theorema Egregium Gauss–Bonnet theorem Gauss–Codazzi equation Gaussian curvature Genus of a closed surface Geodesic Gradient Index juggling Inner product matrix Intrinsic derivative Invariant Invariant time derivative Jolt of a particle Kronecker symbol Levi-Civita symbol Mean curvature Metric tensor Metrics Minimal surface Normal derivative Normal velocity Orientation of a coordinate system Orientation preserving coordinate change Relative invariant Relative tensor Repeated index Ricci tensor Riemann space Riemann–Christoffel tensor Scalar Scalar curvature Second groundform Shift tensor Stokes’ theorem Surface divergence Surface Laplacian Surge of a particle Tangential coordinate velocity Tensor property Theorema Egregium Third groundform Thomas formula Time evolution of integrals Torsion of a curve Total curvature Variant Vector Parallelism along a curve Permutation symbol Polar coordinates Position vector Principal curvatures Principal normal Quotient theorem Radius vector Rayleigh quotient Rectilinear coordinates Vector curvature normal Vector curvature tensor Velocity of an interface Volume element Voss–Weyl formula Weingarten’s formula Applications: Differenital Geometry, Relativity
Views: 22387 MathTheBeautiful
Self-adjoint operator
 
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If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 Self-adjoint operator In mathematics, a self-adjoint operator on a complex vector space V with inner product is a linear map A (from V to itself) that is its own adjoint: .If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is Hermitian, i.e., equal to its conjugate transpose A*. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=HdfQxsafU9E
Views: 641 WikiAudio
Mathematics of Quantum 13 (Bra-Ket Notation, Inner Product)
 
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Mathematical Structure of Quantum Mechanics 13 by Kaveh Inner Product Bras and Kets Notation Delta Function
Views: 1565 Kaveh Mozafari