All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two
Keyword(s):
Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation.
A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
2004 ◽
Vol 384
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pp. 43-54
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Keyword(s):
Keyword(s):
2013 ◽
Vol 56
(9)
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pp. 1795-1820
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2009 ◽
Vol 86
(1)
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pp. 1-15
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2010 ◽
Vol 40
(3)
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pp. 825-848
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