Stein equation. A Stein equation with respect to square matrix X has the form AXB-X+Q = 0, where A. B and Q are constant square matrices. (a) When does this equation have a unique solution? (b) Figure out all solutions in case of A [] B= 12 -4 (c) Construct a counter example in which no solution exists.

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5. Stein equation. A Stein equation with respect to square
AXB-X+Q= 0, where A,
matrix X has the form
B and Q are constant square matrices.
(a) When does this equation have a unique solution?
(b) Figure out all solutions in case of A =
-4).
(c) Construct a counter example in which no solution
exists.
(d) Can you extend your method to general case?
B=
-9-1
01
Transcribed Image Text:5. Stein equation. A Stein equation with respect to square AXB-X+Q= 0, where A, matrix X has the form B and Q are constant square matrices. (a) When does this equation have a unique solution? (b) Figure out all solutions in case of A = -4). (c) Construct a counter example in which no solution exists. (d) Can you extend your method to general case? B= -9-1 01
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