A theorem for complex symmetric matrices revisited

In this contribution we will revisit the celebrated theorem that every square matrix is similar to a (complex) symmetric matrix and that every symmetric matrix is orthogonally similar to a given normal canonical form. Specifically we will re‐examine the proof as well as the derivation of an explicit n ‐dimensional complex symmetric form. We will extend the formula to incorporate the various powers of the original normal form, a derivation not previously provided. Some examples of these complex symmetric forms in chemical and physical applications are indicated. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009