Скачать или смотреть Orthogonal Diagonalization Explained | Linear Algebra

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We introduce orthogonal similarity and orthogonal diagonalization. We'll prove the Fundamental Theorem of Symmetric Matrices establishing the equivalence between symmetric matrices and orthogonal diagonalizability. We'll go over how to orthogonally diagonalize a matrix step by step by finding the eigenvectors and using the Gram-Schmidt process, and complete an example of the orthogonal diagonalization of a 3x3 matrix. #linearalgebra

Diagonalizing Matrices:    • Diagonalizing Matrices and Diagonalizabili...  
Gram-Schmidt Orthonormalization Process:    • Gram-Schmidt Orthogonalization (Proof and ...  

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0:00 Intro
0:45 Orthogonal Similarity
1:33 Symmetry of Orthogonal Similarity
2:33 Orthogonally Diagonalizable
3:43 Eigenvectors from Distinct Eigenspaces are Orthogonal
5:50 Fundamental Theorem of Symmetric Matrices
11:37 Step by Step Orthogonal Diagonalization
12:39 Orthogonal Diagonalization of a 3x3 Matrix
15:53 Conclusion