example-of-diagonalizing-a-symmetric-matrix-spectral-theorem

Linear Algebra: For the real symmetric matrix [3 2 / 2 3], 1) verify that all eigenvalues are real, 2) show that eigenvectors for distinct eigenvalues are orthogonal with respect to the standard inner product, and 3) find an orthogonal matrix P such that P^{-1}AP = D is diagonal. The Spectral Theorem states that every symmetric matrix can be put into real diagonal form using an orthogonal change of basis matrix (or there is an orthonormal basis of eigenvectors).

Tagged under: Mathematics,linear,algebra,symmetric,matrix,diagonal,orthogonal,change,basis,orthonormal,eigenvector,eigenvalue,null,space,spectral,theorem

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