symmetric matrix A, meaning A= AT. It is a beautiful story which carries the beautiful name the spectral theorem: Theorem 1 (The spectral theorem). If Ais an n nsym-metric matrix then (1)All eigenvalues of Aare real. (2) Ais orthogonally diagonalizable: A= PDPT where P is an orthogonal matrix and Dis real diagonal.
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Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. 10 3 3 2 Enter the matrices P and D below. Get more help from Chegg Solve it with our algebra problem solver and calculator
Any m by n matrix X can be factored into X = U*S*V', where U is an m by m orthogonal matrix, S is an m by n diagonal matrix, and V is an n by n orthogonal matrix. Another way to put this is that ANY matrix can be viewed as a rigid rotation (with possible reflection), followed by an axis scaling, followed by another rigid rotation/reflection.