Singular Value and Eigenvalue Distribution of a Matrix-Sequence

Abstract

Throughout this book, a matrix-sequence (or sequence of matrices) is any sequence of the form $\{A_n\}_n$, where $A_n\in \mathbb C^{n\times n}$ and n varies in some infinite subset of $\mathbb N$. This chapter introduces the notion of (asymptotic) singular value and eigenvalue distribution for a matrix-sequence, as well as other related concepts such as clustering and attraction. A special attention is devoted to the so-called zero-distributed sequences, which play a central role in the theory of GLT sequences.