Relations between least-squares and least-rank solutions of the matrix equation A×B = C

Yongge Tian; Hongxing Wang

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Relations between least-squares and least-rank solutions of the matrix equation A×B = C

机译：矩阵方程A×B = C的最小二乘和最小秩解之间的关系

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A matrix X is called a least-squares solution of the matrix equation A×B = C if it minimizes the F-norm of C - A×B, a least-rank solution of A×B = C if it minimizes the rank of C - A×B. These two types of solution are not necessarily the same. In this paper, we establish necessary and sufficient conditions for the two types of solutions to coincide by using some matrix rank formulas and nested decompositions of matrices.

机译：如果矩阵X最小化C-A×B的F范数，则称为矩阵方程A×B = C的最小二乘解;如果矩阵X的秩最小，则称为A×B = C的最小秩解。 C-A×B。这两种类型的解决方案不一定相同。在本文中，我们通过使用一些矩阵秩公式和矩阵的嵌套分解，为两种类型的解建立一致的必要和充分条件。

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《Applied mathematics and computation》 |2013年第20期|共9页
作者
Yongge Tian; Hongxing Wang;
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正文语种 eng
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Matrix equation; Least-squares solution; Least-rank solution; Moore–Penrose inverse; Matrix decomposition; Rank formula;

机译：矩阵方程;最小二乘解;最小秩解;Moore-Penrose逆;矩阵分解;Rank公式;

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Relations between least-squares and least-rank solutions of the matrix equation A×B = C

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