Geodesic
Determinant preserving transformations on symmetric matrix spaces
The electronic journal of linear algebra, Tome 11 (2004), pp. 205-211.

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

Summary: Let $Sn(F)$ be the vector space of n * n symmetric matrices over a field F (with certain restrictions on cardinality and characteristic). The transformations A' on the space which satisfy one of the following conditions: 1. $det(A + y"B) = $det(A'$(A) + y$"A'$(B))$ for all A, B $2 Sn(F)$ and y" 2 F; 2. A' is surjective and $det(A + y"B) = $det(A'$(A) + y$"A'$(B))$ for all A, B and two specific y"; 3. A' is additive and preserves determinant are characterized.
Classification : 15A03, 15A04
Keywords: linear preserving problem, rank, symmetric matrix, determinant 
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     author = {Cao, Chongguang and Tang, Xiaomin},
     title = {Determinant preserving transformations on symmetric matrix spaces},
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Cao, Chongguang; Tang, Xiaomin. Determinant preserving transformations on symmetric matrix spaces. The electronic journal of linear algebra, Tome 11 (2004), pp. 205-211. http://geodesic.mathdoc.fr/item/ELA_2004__11__a5/