Spectral shorted matrices

J. ANTEZANA, G. CORACH Y D. STOJANOFF

LINEAR ALGEBRA AND ITS APPLICATIONS

Birkhauser

Año: 2004 vol. 381 p. 197 - 217

0024-3795

Given a $n\times n$ positive semidefinite matrix $A$ and a subspace $\ese$ of$\mathbb {C}^{n}$, $\Sigma (\ese, A) $ denotes the shorted matrix of $A$ to $\ese$.We consider the notion of $spectral$ $shorted$ matrix$$\rho (\ese, A) = \lim _{m \to \infty } \Sigma (\ese, A^m )^{1/m}.$$We completely characterize this martix in terms of $\ese$ and the spectrum andthe eigenspaces of $A$. We show the relation of this notion with the spectral orderof matrices and the Kolmogorov's complexity of $A$ to a vector $\xi \in \mathbb {C}^{n}$.