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 and invariant subspaces. Description of normal operators on real inner product spaces.

Views: 801
Sheldon Axler

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

Views: 470
LadislauFernandes

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

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

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.

Views: 99
ComputerVisionFoundation Videos

Linear Algebra 24, Dot Product as a Linear Operator 1

Views: 503
LadislauFernandes

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

Views: 852
LadislauFernandes

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

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.

Views: 130
Sukkur IBA University- Mathematics

Views: 43262
Toby Driscoll

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

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

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

Views: 25791
Jonathan Sprinkle

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

Views: 405
118yt118

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. Square roots of operators. Characterization of positive operators. Each positive operator has a unique positive square root.

Views: 1422
Sheldon Axler

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Mathematical Structure of Quantum Mechanics 2 by Kaveh in simple words
Inner Product
Bra-Ket

Views: 1277
Kaveh Mozafari

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.

Views: 328
Mathematics Analysis

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

Subject:-Mathematics
Paper:- Functional Analysis
Principal Investigator:-Prof.M. Majumdar

Views: 1920
Vidya-mitra

Views: 4881
nptelhrd

Mathematical Structure of Quantum Mechanics 15 By Kaveh
Operators
Identity
Other Product

Views: 517
Kaveh Mozafari

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

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*.
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Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=HdfQxsafU9E

Views: 641
WikiAudio

Mathematical Structure of Quantum Mechanics 13 by Kaveh
Inner Product
Bras and Kets Notation
Delta Function

Views: 1565
Kaveh Mozafari