In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry. (Wikipedia).
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
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
In this last part of the orthogonality extravaganza, I show how to use our orthogonality-formula to find the full Fourier series of a function. I also show to what function the Fourier series converges too. In a future video, I'll show you how to find the Fourier sine/cosine series of a fu
From playlist Orthogonality
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)
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
11J Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Determine if the Vectors are Orthogonal
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determine if the Vectors are Orthogonal
From playlist Calculus
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
From playlist Linear Algebra Ch 6
Orthogonal complements. The direct sum of a subspace and its orthogonal complement. Dimension of the orthogonal complement. The orthogonal complement of the orthogonal complement.
From playlist Linear Algebra Done Right
Gram-Schmidt Orthogonalization for Three or More Vectors
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
Orthogonal complement of the orthogonal complement | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/lin-alg-orthogonal-complement-of-the-orthogonal-complement Finding that the orthogonal complement of the ort
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
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
14. Orthogonal Vectors and Subspaces
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 14. Orthogonal Vectors and Subspaces License: Creative Commons BY-NC-SA More information at ht
From playlist MIT 18.06 Linear Algebra, Spring 2005
36 entangled officers of Euler: A quantum solution to a classically... by Arul Lakshminarayan
Colloquium: 36 entangled officers of Euler: A quantum solution to a classically impossible problem Speaker: Arul Lakshminarayan (IIT Madras, Chennai) Date: Mon, 06 June 2022, 15:30 to 17:00 Venue: Online and Madhava Lecture Hall Abstract The 36 officers problem of Euler is a well-known i
From playlist ICTS Colloquia
P2L04_15Oct2020 (Tut6, Q6,11) (un-edited)
P2L04_15Oct2020: 4th lecture, zoom (un-edited), Tut 6, Q6 & 11 (recorded 15 Oct 2020) Quest 6) 23a 00:00 - 02:25 23b 02:25 - 08:15 23c 08:39 - 13:05 23d 13:05 - 16:30 23e 16:40 - 24:30 25:03 - 25:26 "How do we justify 23d" 24a 27:00 - 28:05 24b 28
From playlist Part 2 lectures (2020 zoom)
3. Orthonormal Columns in Q Give Q'Q = I
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k This lecture focus
From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
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
(4.1.3) Orthogonality of Eigenfunctions Theorem and Proof
This video explains and proves a theorem on the orthogonality of eigenfunctions. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
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