Rigidity and Shrinkability of Diagonalizable Matrices
Dimitris Karayannakis *
Department of Informatics Engineering, TEI of Crete, Heraklion 71004, Greece.
Maria-Evgenia Xezonaki
Department of Informatics and Telecommunications, University of Athens, Athens 157 84, Greece.
*Author to whom correspondence should be addressed.
Abstract
We introduce the seemingly new concept of a rigid matrix based on the comparison of its sparsity to the sparsity of the natural powers of the matrix. Our results could be useful as a usage guide in the scheduling of various iterative algorithms that appear in numerical linear algebra. Especially in Sparse matrix-vector multiplication and they could also be used in matrix norm error analysis.
Keywords: Sparse matrix, diagonalizable matrix, matricial limits, matrix norms.