Solving for unknown matrix X

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Jin
Jin 2023-4-5
回答： Hiro Yoshino 2023-4-5
Solve matrix equation AXB=C, solve for matrix X
Hey. Can some of you help me with this task? I've tried multiple ways to solve this but I just can't figure out how to solve for the unknown matrix X.
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Thank you.

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Hiro Yoshino
Hiro Yoshino 2023-4-5
Ran in:
I would use a pesudoinverse:
A = [6 4;6 1; 1 2; 6 4]
A = 4×2
6 4 6 1 1 2 6 4
B = [8 8 6 7 5; 8 8 1 6 0; 1 4 3 8 7]
B = 3×5
8 8 6 7 5 8 8 1 6 0 1 4 3 8 7
C = [18042 21288 10716 22446 12924; 12768 15024 7593 15795 9099;...
5351 6332 3174 6697 3854; 18042 21288 10716 22446 12924]
C = 4×5
18042 21288 10716 22446 12924 12768 15024 7593 15795 9099 5351 6332 3174 6697 3854 18042 21288 10716 22446 12924
How about thinking of Moore-Penrose pseudoinverse?
X = pinv(A)*C*pinv(B)
X = 2×3
111.0000 105.0000 107.0000 101.0000 105.0000 110.0000
Check if this works well:
A*X*B - C
ans = 4×5
1.0e-10 * 0.1091 0.1091 0.0364 0.1091 0.0364 0.1091 0.1273 0.0364 0.1091 0.0364 0.0182 0.0182 0.0091 0.0182 0.0045 0.1091 0.1091 0.0364 0.1091 0.0364
Floating-point relative accuracy is given by
eps
ans = 2.2204e-16

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