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**P**such that

**P**[tex]^{-1}[/tex]

**A**

**P**is diagonal, i.e.

**P**[tex]^{T}[/tex]

**A**

**P**(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**=

[

**U**

**0**

**U**]

[

**0**

**0**

**0**]

[

**U**

**0**

**U**]

where

**U**is square matrix and

**0**is 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?