Geodesic
On (con)similarities and congruences between $A$ and $A^*$, $A^T$ or $\bar A$
The electronic journal of linear algebra, Tome 17 (2008), pp. 258-283.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A unifying approach is presented between similarity, consimilarity, T congruence and *congruence of a matrix A to a symmetric, to a Hermitian or to a real matrix. Also studied are similarity consimilarity, T congruence and *congruence of a matrix A to A $\ast $, A T , and A. Attempts are made to find special (con)similarities and congruences, as well as to find connections between these classes of maps. For example, it is shown that if AA is nonderogatory and nonsingular, then the consimilarities between A and A T are precisely the Hermitian similarities between AA and (AA) $\ast $.
Classification : 15A21, 15A24, 15A48, 15A57, 15A63
Keywords: similarities, consimilarities, T congruences, $\ast $congruences, canonical forms, involutions, coninvolutions 
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     author = {Vermeer, J.},
     title = {On (con)similarities and congruences between $A$ and $A^*$, $A^T$ or $\bar A$},
     journal = {The electronic journal of linear algebra},
     pages = {258--283},
     publisher = {mathdoc},
     volume = {17},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2008__17__a26/}
}
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Vermeer, J. On (con)similarities and congruences between $A$ and $A^*$, $A^T$ or $\bar A$. The electronic journal of linear algebra, Tome 17 (2008), pp. 258-283. http://geodesic.mathdoc.fr/item/ELA_2008__17__a26/