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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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