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This paper studies the following two problem:
Problem Ⅰ. Given $X,B∈R^{n×m}$, find $A∈P_{s,n}$, such that $AX=B$, where
$P_{s,n}$={$A∈SR^{n×n}|x^T AX≥0,∀S^Tx=0$ , for given $S∈R^{n×p}_p$}.
Problem Ⅱ. Given $A^*∈R^{n×n}$, find $\hat{A}∈S_E$, such that $||A^*-\hat{A}||$=inf$_{A∈S_E}||A^*-A||$ where $S_E$ denotes the solutions set of Problem Ⅰ.
The necessary and sufficient conditions for the solvability of Problem Ⅰ, the expression of the general solution of Problem Ⅰ and the solution of Problem Ⅱ are given for two case. For the general case, the equivalent form of conditions for the solvability of Problem Ⅰ is given.
This paper studies the following two problem:
Problem Ⅰ. Given $X,B∈R^{n×m}$, find $A∈P_{s,n}$, such that $AX=B$, where
$P_{s,n}$={$A∈SR^{n×n}|x^T AX≥0,∀S^Tx=0$ , for given $S∈R^{n×p}_p$}.
Problem Ⅱ. Given $A^*∈R^{n×n}$, find $\hat{A}∈S_E$, such that $||A^*-\hat{A}||$=inf$_{A∈S_E}||A^*-A||$ where $S_E$ denotes the solutions set of Problem Ⅰ.
The necessary and sufficient conditions for the solvability of Problem Ⅰ, the expression of the general solution of Problem Ⅰ and the solution of Problem Ⅱ are given for two case. For the general case, the equivalent form of conditions for the solvability of Problem Ⅰ is given.