IJPAM: Volume 15, No. 1 (2004)

BAND DIAGONAL MATRICES AND UNITARY
OR ORTHOGONAL TRANSFORMATIONS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.A matrix $A = (a_{ij})\in M(n\times n,{\Bbb C})$ is said to be $a$-diagonal for some integer $a$ with $0<a<n$ if $a_{ij} = 0$ for all $i,j$ with $\vert i-j\vert > a$. Here we prove that if $n^2 \ge 2n+2a(2n-a-1)$ a general $A$ cannot be put in $a$-diagonal form using unitary transformations. We also consider the same problem for real matrices, up to orthogonal transformations.

Received: May 5, 2004

AMS Subject Classification: 15A12

Key Words and Phrases: tridiagonal matrix, band diagonal operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 1