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A theorem for complex symmetric matrices revisited
Author(s) -
Brändas Erkki J.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22097
Subject(s) - matrix (chemical analysis) , complex matrix , mathematics , pure mathematics , square matrix , symmetric matrix , algebra over a field , combinatorics , quantum mechanics , physics , chemistry , eigenvalues and eigenvectors , chromatography
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