Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive...Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.展开更多
Let P∈C^( m×m )and Q∈C^( n×n) be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexiv...Let P∈C^( m×m )and Q∈C^( n×n) be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(anti-reflexive)if P XQ=X(P XQ=−X).In this paper,the least squares solution of the matrix equation AXB=C subject to{P,Q,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2.展开更多
基金Supported by the Education Department Foundation of Hebei Province（QN2015218） Supported by the Natural Science Foundation of Hebei Province（A2015403050）
文摘Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.
基金Supported by the Education Department Foundation of Hebei Province(Grant No.QN2015218).
文摘Let P∈C^( m×m )and Q∈C^( n×n) be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(anti-reflexive)if P XQ=X(P XQ=−X).In this paper,the least squares solution of the matrix equation AXB=C subject to{P,Q,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2.
