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In mathematics, the spectral radius of a square matrix or a bounded linear operator is the supremum among the absolute values of the elements in its spectrum.

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If the spectral radius of matrix $A$ is less than $1$, how to construct a positive definite ...

I'll follow the suggestions in the comments and post my comment as an answer: Take your favourite positive definite matrix $P$ and define $Q := \sum_{k=0}^\infty (A^{\operatorname{H}})^k P A^k$; note …
Jochen Glueck's user avatar