Orthogonality and Orthonormality
We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one
From playlist Mathematics (All Of It)
Math 060 Fall 2017 111317C Orthonormal Bases
Motivation: how to obtain the coordinate vector with respect to a given basis? Definition: orthogonal set. Example. Orthogonal implies linearly independent. Orthonormal sets. Example of an orthonormal set. Definition: orthonormal basis. Properties of orthonormal bases. Example: Fou
From playlist Course 4: Linear Algebra (Fall 2017)
Linear Algebra: Orthonormal Basis
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/ More on unit vectors: https://www.youtube.com/watch?v=C6EYJVBYXIo
From playlist Basics: Linear Algebra
Linear Algebra - Lecture 39 - Orthonormal Sets
In this lecture, we discuss orthonormal sets of vectors. We investigate matrices with orthonormal columns. We also define an orthogonal matrix.
From playlist Linear Algebra Lectures
Math 139 Fourier Analysis Lecture 31: Fourier Analysis on Finite Abelian Groups
Finite abelian groups; characters; dual group. Characters form an orthonormal family: cancellation property (moment condition) of characters; proof of orthonormality; the dual group is an orthonormal basis for the space of functions on the group. Linear algebra: spectral theorem (given a
From playlist Course 8: Fourier Analysis
Orthonormal bases. The Gram-Schmidt Procedure. Schuur's Theorem on upper-triangular matrix with respect to an orthonormal basis. The Riesz Representation Theorem.
From playlist Linear Algebra Done Right
Linear Algebra: Given an orthonormal basis of R^n, we present a quick method for finding coefficients of linear combination in terms of the basis. We also give an analogue of Parseval's Identity, which relates these coefficients to the squared length of the vector.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Orthogonal and Orthonormal Sets of Vectors
This video defines orthogonal and orthonormal sets of vectors.
From playlist Orthogonal and Orthonormal Sets of Vectors
Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger
In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb
From playlist Universal Hyperbolic Geometry
Lecture 15: Orthonormal Bases and Fourier Series
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=Yb69dAq4uh8&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Lecture 14: Basic Hilbert Space Theory
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=EBdgFFf54U0&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
17. Orthogonal Matrices and Gram-Schmidt
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 17. Orthogonal Matrices and Gram-Schmidt License: Creative Commons BY-NC-SA More information a
From playlist MIT 18.06 Linear Algebra, Spring 2005
Linear Algebra 20j: The Dot Product, Matrix Multiplication, and the Magic of Orthogonal Matrices
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=PBMyBVPRtKA&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
The Complex Spectral Theorem and the Real Spectral Theorem, with examples.
From playlist Linear Algebra Done Right
RT8.2. Finite Groups: Classification of Irreducibles
Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) usin
From playlist Representation Theory