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An identity for matrix rings with involution

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
174
Identifiers
DOI: 10.1016/0024-3795(92)90044-b

Abstract

Abstract The main result examines when the expression G n ( X, Y) = X n−1 Y + X n− 2 YX + … + YX n−1 gives an identity for M n ( F) with involution, when X is a (skew-)symmetric nilpotent matrix and Y is any (skew-)symmetric matrix. For transpose involution, G n ( X, Y ) = 0 when X is any nilpotent symmetric matrix and Y is skew-symmetric.

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