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Orthogonal Matrices (Definition & Theorems)
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Here we explore matrices whose columns form an orthonormal set!
Theorem 1: The columns of an mxn matrix Q form an orthonormal set IFF (transpose of Q)Q=I.
Theorem 2: A square matrix Q is orthogonal IFF (inverse of Q)=(transpose of Q).
Theorem 1: The columns of an mxn matrix Q form an orthonormal set IFF (transpose of Q)Q=I.
Theorem 2: A square matrix Q is orthogonal IFF (inverse of Q)=(transpose of Q).