Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on solutions of the matrix equation AXB=C   This paper deals with necessary and sufficient condition for consistency of
the matrix equation $AXB = C$. We will be concerned with the minimal number of
free parameters in Penrose's formula $X = A^(1)CB^(1) + Y - A^(1)AYBB^(1)$ for
obtaining the general solution of the matrix equation and we will establish the
relation between the minimal number of free parameters and the ranks of the
matrices A and B. The solution is described in the terms of Rohde's general
form of the {1}-inverse of the matrices A and B. We will also use Kronecker
product to transform the matrix equation $AXB = C$ into the linear system $(B^T
\otimes A)vecX = vec C$.

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The categories of this paper are: hep-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con