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Let P∈Cm×m and Q∈Cn×n be Hermitian and {k+1}-potent matrices; that is, Pk+1=P=P⁎ and Qk+1=Q=Q⁎, where ·⁎ stands for the conjugate transpose of a matrix. A matrix X∈Cm×n is called {P,Q,k+1}-reflexive (antireflexive) if PXQ=X (PXQ=-X). In this paper, the system of matrix equations AX=C and XB=D subject to {P,Q,k+1}-reflexive and antireflexive constraints is studied by converting into two simpler cases: k=1 and k=2. We give the solvability conditions and the general solution to this system; in addition, the least squares solution is derived; finally, the associated optimal approximation problem for a given matrix is considered

mathematical problems in engineering

The<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">{</mml:mo><mml:mi>P</mml:mi><mml:mo>,</mml:mo><mml:mi>Q</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn fontstyle="italic">1</mml:mn><mml:mo stretchy="false">}</mml:mo></mml:math>-Reflexive Solution to System of Matrix Equations<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>C</mml:mi></mml:math>,<mml:…

The{P,Q,k+1}-Reflexive Solution to System of Matrix EquationsAX=C,