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The anti-reflexive extremal rank solutions of the matrix equation AX = B
| Content Provider | Semantic Scholar |
|---|---|
| Author | Xiao, Qing-Feng Zhang, Lei |
| Copyright Year | 2012 |
| Abstract | An n × n complex matrix P is said to be a generalized reflection matrix if P∗ = P and P2 = I. An n× n complex matrix A is said to be a anti-reflexive matrix with respect to the generalized reflection matrix P if A = −PAP. We in this paper mainly investigate the anti-reflexive maximal and minimal rank solutions to the matrix equation AX = B. We present necessary and sufficient conditions for the existence of the maximal and minimal rank solutions with anti-reflexive to the matrix equation AX = B. The expressions of such solutions to this system are also given when the solvability conditions are satisfied. In addition, in corresponding the minimal rank solution set to the matrix equation AX = B, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://operator.pmf.ni.ac.rs/www/pmf/publikacije/faac/2012/2012-4-2/faac-4-2-3.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
