Quadratically Normal Matrices of Type 1 and Unitary Similarities between Them

Verification of the unitary similarity between matrices having quadratic minimal polynomials is known to be much cheaper than the use of the general Specht–Pearcy criterion. Such an economy is possible due to the following fact: $n\times n$ matrices $A$ and $B$ with quadratic minimal polynomials are unitarily similar if and only if $A$ and $B$ have the same eigenvalues and the same singular values. It is shown that this fact is also valid for a subclass of matrices with cubic minimal polynomials, namely, quadratically normal matrices of type 1.