Linear Algebra 7.3 Symmetric Matrices and Orthogonal Diagonalization
Автор: Kimberly Brehm
Загружено: 2026-02-27
Просмотров: 33
Описание:
Unlock one of the most elegant results in linear algebra: *every real symmetric matrix can be orthogonally diagonalized**. In this lesson, we break down *why symmetric matrices behave so nicely, how orthogonal diagonalization works, and what it means geometrically.
Whether you're in a first linear algebra course or brushing up for applications in data science, differential equations, or machine learning, this video gives you the intuition and the step‑by‑step structure you need.
Video Chapters:
00:00 Intro
00:08 Symmetric Matrices
02:36 Diagonalizing a Symmetric Matrix (3x3)
09:27 Finding Eigenvalues (4x4)
12:23 Orthogonal Matrices
13:03 An Orthogonal Matrix
13:52 An Orthonormal Set
16:05 Orthogonal Matrices (on your own)
18:56 Orthogonal Diagonalization (2x2)
22:25 Orthogonal Diagonalization (3x3)
35:38 Up Next
Textbook: Elementary Linear Algebra 8e, Ron Larson
Slide Decks: https://bellevueuniversity-my.sharepo...
Playlist: • Linear Algebra (Full Course - Under Produc...
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