Spectral shorted matrices. (Q1430380)

Given an \(n \times n\) positive semidefinite matrix \(A\) and a subspace \(S\) of \(\mathbb{C}^n\), the authors define and study the properties of a positive matrix called spectral shorted matrix of \(A\) by \(S\) \[ \rho(S,A)=\lim_{m \rightarrow \infty} \Sigma(S,A^m)^{1/m}, \] where \(\Sigma(S,A^m)\) is the shorted matrix of \(A^m\). They completely characterize the matrix \(\rho(S,A)\) in terms of the subspace \(S\) and the eigenspaces of \(A\). They also show the relation of this notion with the spectral order of matrices and the Kolmogorov's complexity of \(A\) to a vector \(v \in \mathbb{C}^n\).