Orthogonal Diagonalization Explained | Linear Algebra

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

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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

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Elementary Linear Algebra by Anton

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[talastra]

Extremely lucid exposition. I'm always impressed by the precision of your speaking; you don't cut corners, or say things like "the vector" when you mean "the orthogonally diagonalized vector" (despite the obvious temptation. It keeps things unambiguously clear and exact.