Re: diagonalization using unitary matrices

math_think <arielguerreiro@xxxxxxxxx> writes:

Dear All

I have got a self adjoint square matrix with real coefficients and I
need to find the unitary matrix which diagonalizes the first.
According to the spectral theorem such unitary matrix exists but the
traditional method of diagonalization, which consists in finding the
eigenvectors and putting them as the columns of a diagonalization
matrix does not generate necessarily an unitary matrix.

For distinct eigenvalues the eigenvectors are automatically orthogonal, and
all you need to do is normalize them to have 2-norm 1. If there are
several eigenvectors for the same eigenvalue, use Gram-Schmidt to get
orthonormal eigenvectors.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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