Orthogonal bases are easy to work with!
Description: We can extend the idea of two orthogonal vectors to an orthogonal set of vectors. Then, if you have an orthogonal basis opposed to a normal basis, trying to expand a vector in the basis is a much easier task; each coefficient is determined by a couple dot products only. Lear
From playlist Linear Algebra (Full Course)
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)
This is the first video of a linear algebra-series on orthogonality. In this video, I define the notion of orthogonal sets, then show that an orthogonal set without the 0 vector is linearly independent, and finally I show that it's easy to calculate the coordinates of a vector in terms of
From playlist Orthogonality
Find an Orthogonal Projection of a Vector Onto a Line Given an Orthogonal Basis (R2)
This video explains how t use the orthogonal projection formula given subset with an orthogonal basis. The distance from the vector to the line is also found.
From playlist Orthogonal and Orthonormal Sets of Vectors
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
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 7.1 Orthogonal Matrices
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
In this video, I define the concept of orthogonal projection of a vector on a line (and on more general subspaces), derive a very nice formula for it, and show why orthogonal projections are so useful. You might even see the hugging formula again. Enjoy! This is the second part of the ort
From playlist Orthogonality
Math 060 Fall 2017 111517C Orthonormal Bases, Orthogonal Matrices, and Method of Least Squares
Definition of orthogonal matrices. Example: rotation matrix. Properties: Q orthogonal if and only if its transpose is its inverse. Q orthogonal implies it is an isometry; that it is isogonal (preserves angles). Theorem: How to find, given a vector in an inner product space, the closest
From playlist Course 4: Linear Algebra (Fall 2017)
Linear Algebra 6.3 Gram-Schmidt Process; QR-Decomposition
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
Mod-01 Lec-07 Cauchy Schwaz Inequality and Orthogonal Sets
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
P2L5 19Oct2020 (Tut6: Q7-11) edited
Tut 6 00:00 - 06:25 Q7 06:25 - 07:40 Discussion T6-Support.ppt 08:00 - 17:25 Q8) 17:30 - 27:40 Q9) 27:45 - 30:11 Q10-21a 30:15 - 31:00 Q10-21b 31:00 - 32:48 Q10-21c 32:48 - 34:00 Q10-21d 34:00 - 34:50 Q10-21e 34:50 - 40:30 (Q11-partial) 40:30 -
From playlist Part 2 lectures (2020 zoom)
Using Gram-Schmidt to orthogonalize a basis
Description: I love having an orthogonal basis, but often I only have a regular old basis. Gram-Schmidt is a process to transform a basis for a subspace into an orthogonal basis for the same subspace Learning Objectives: 1) Given a basis of vectors for a subspace W, find an orthogonal bas
From playlist Linear Algebra (Full Course)
29. Singular Value Decomposition
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 29. Singular Value Decomposition License: Creative Commons BY-NC-SA More information at https:
From playlist MIT 18.06 Linear Algebra, Spring 2005
Spectral Theorem for Real Matrices: General nxn Case
Linear Algebra: We state and prove the Spectral Theorem for real vector spaces. That is, if A is a real nxn symmetric matrix, we show that A can be diagonalized using an orthogonal matrix. The proof refers to the 2x2 case and to results from the video Beyond Eigenspaces: Real Invariant
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Stefan Sauter: A Family of Crouzeix-Raviart Non-Conforming Finite ...
Stefan Sauter: A Family of Crouzeix-Raviart Non-Conforming Finite Elements in Two- and Three Spatial Dimensions The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. (17.02.2017) In t
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Linear Algebra - Lecture 38 - Orthogonal Sets
In this lecture, we discuss orthogonal sets of vectors. We also investigate the idea of an orthogonal basis, as well as orthogonal projections of vectors.
From playlist Linear Algebra Lectures
Introduction to the Gram-Schmidt Orthogonalization Procedure
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 4 Linear Algebra: Inner Products
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra