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Orthogonal Matrices, Change of Orthonormal Basis - Linear Algebra
Repost
2 days ago
62
Science
Education
linear algebra
orthogonal matrices
orthonormal basis
orthogonal diagonalization of symmetric matrices
orthogonal
linear algebra orthogonal matrices
change of orthonormal basis
change of basis
linear algebra (field of study)
This video explains what an orthogonal matrix is, including definition, meaning, formula, how to check it with examples (e.g. 2x2 and 3x3) and the condition. It also explains how to derive the an orthogonal transition matrix for changing between orthogonal or orthonormal bases.
0:00 Orthogonal matrices
3:14 Inverse of an orthogonal matrix, properties
7:02 Orthogonal matrices as linear operators
9:46 Orthonormal basis
11:49 Change of orthonormal basis
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