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Roth's Removal Rule

If the matrices A, X, B, and C satisfy

AX-XB=C,

then

[I X; 0 I][A C; 0 B][I -X; 0 I]=[A 0; 0 B],

where I is the identity matrix.

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References

Roth, W. E. "The Equations AX-YB=C and AX-XB=C in Matrices." Proc. Amer. Math. Soc. 3, 392-396, 1952.Turnbull, H. W. and Aitken, A. C. An Introduction to the Theory of Canonical Matrices. New York: Dover, p. 422, 1961.

Referenced on Wolfram|Alpha

Roth's Removal Rule

Cite this as:

Weisstein, Eric W. "Roth's Removal Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RothsRemovalRule.html

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