59. Orthogonally Diagonalizable Matrices A matrix A is orthogonally diagonalizable if there is an orthogonal ma- trix P that diagonalizes it. Show that the matrix A - (: }) [4 21 2 is orthogonally diagonalizable. HINT: Symmetric matrices have orthogonal eigenvectors.

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 27CM: Use the Gram-Schmidt orthonormalization process to find an orthogonal matrix P such that PTAP...
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59. Orthogonally Diagonalizable Matrices A matrix A is
orthogonally diagonalizable if there is an orthogonal ma-
trix P that diagonalizes it. Show that the matrix
A - (: })
[4 21
2
is orthogonally diagonalizable. HINT: Symmetric matrices
have orthogonal eigenvectors.
Transcribed Image Text:59. Orthogonally Diagonalizable Matrices A matrix A is orthogonally diagonalizable if there is an orthogonal ma- trix P that diagonalizes it. Show that the matrix A - (: }) [4 21 2 is orthogonally diagonalizable. HINT: Symmetric matrices have orthogonal eigenvectors.
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