# singular values

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Let A be a (m x m) Normal Matrix

a) Calculate the singular values of A as a function of the eigenvalutes of A.

b) Prove that the eigenvalues of A are all purely imaginary if and only if A is anti-symmetric (A^H = -A)

https://brainmass.com/math/complex-analysis/singular-values-matrix-288792

#### Solution Preview

(a) The spectral theorem can be applied to obtain unitary diagonalization of A = UΛU * . Therefore,

sqrt{A*A} = U |Λ| U*

and so the singular values are simply the absolute values of the ...

#### Solution Summary

The expert calculate the singular values in this case.The eigenvalues of A are all proved.

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