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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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Projecting onto space of matrices with spectral radius less than one

Consider the space $$ S = \left\{ A \in \mathbb{R}^{n \times n} : \mathrm{SpectralRadius}(|A|) \leq 1 \right\}$$ where $|A|$ is the entry-wise absolute value. Given a matrix $M \in \mathbb{R}^{n\times …