Submitted:
14 May 2026
Posted:
15 May 2026
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Abstract
Suppose \( A=I-PQ^T, \) where both \( P \)and \( Q \) are \( n\times 3 \) complex matrices and det\( (Q^T P)\neq 0 \). By analyzing the Jordan canonical form of the coefficient matrix \( A, \) we find all the anti-commuting solutions \( X, \) which satisfy \( AX=-XA, \) of the Yang-Baxter-like matrix equation(YBME) \( AXA=XAX \).
Keywords:
Yang-Baxter-like matrix equation
; rank-three matrix
; Jordan canonical form
; anticommuting solutions
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