Zero patterns and unitary similarity

A subspace of the space, L(n), of traceless complex n x n matrices can be specified by requiring that the entries at some positions (i, j) be zero. The set, I, of these positions is a (zero) pattern and the corresponding subspace of L(n) is denoted by L(I) (n). A pattern I is universal if every matrix in L(n) is unitarily similar to some matrix in L(I)(n). The problem of describing the universal patterns is raised, solved in full for n <= 3, and partial results obtained for n = 4. Two infinite families of universal patterns are constructed. They give two analogues of Schur's triangularization theorem. (C) 2009 Elsevier Inc. All rights reserved.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000278476100005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)0ARTICLE151-8032