If I haveGiven matrices $A, B, C' \in \Bbb R^{2 \times 6}$, where $'$ denotes matrix transposition, and matrix $L \in \Bbb R^{2 \times 2}$, how can one solve the following linear matrix equation: ACXC'A' - BCXC'B' = L where: in $X \in \Bbb R^{2 \times 2}$?
X: the variable matrix [2x2]
A: a known matrix [2x6], A': The A transpose matrix.
B: a known matrix [2x6], B': The B transpose matrix.
C: a known matrix [6x2], C': The C transpose matrix.
L: the second equation part. [2x2]
$$ ACXC'A' - BCXC'B' = L $$
How can Isolate X Matrix solve it? Maybe I should mention that X is a covariance matrix that should be positive definite or semi-definite. Is$X$ is a covariance matrix that should be positive definite or semidefinite. Is there any standard solution to ensure getting correct values?
