According to the spectral theorem for self-adjoint operators you can find a matrix(adsbygoogle = window.adsbygoogle || []).push({}); Psuch thatP[tex]^{-1}[/tex]APis diagonal, i.e.P[tex]^{T}[/tex]AP(P can be shown to be orthogonal). I'm not sure what the result is if the same can be done for the following square (size n X n) and symmetric matrix of the form:

A=

[U0U]

[000]

[U0U]

whereUis square matrix and0is a matrix of zeros.

If I am not mistaken the solution is that the columns of P are simply the eigenvectors of A??? can anyone confirm this?

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# Regarding Diagonalization of Matrix by Spectral Theorem

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