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Results tagged with matrix-equations
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user 22277
Equations whose unknown is a matrix, such as, for instance, algebraic Riccati equations $XAX+XB+CX+D=0$ or matrix differential equations (e.g. $\dot X(t)=AX(t)$. This tag is *not* meant for general systems of linear equations $Ax=b$.
5
votes
A truncated "geometric" matrix series
With meager loss of generality, let's first assume that $A,C$ are diagonalizable so that $A=RDR^{-1},C=SES^{-1}$ where $R,S$ are invertible and $D,E$ are diagonal.
Then $$\sum_{k=0}^{N-1}A^kBC^k=\sum_ …
6
votes
Sprinkling signs in unitary matrices
I am able to quickly and easily compute counterexamples in both the unitary case and the orthogonal case numerically.
To do this, one should have access to automatic differentiation because I we not w …