Vol. 61, No. 1, 1975

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ISSN: 0030-8730
Kato-Taussky-Wielandt commutator relations and characteristic curves

Fergus John Gaines

Vol. 61 (1975), No. 1, 121–128
Abstract

Let A and B be n × n matrices with elements in a field and let ΔAB = AB BA. Let fk(x) = x2K+1 c1x2K1 + c2x2K3 + + (1)KcKx, where the ci are in and K = k(k 1)2. In this paper we examine the consequences of the relation fkA)B = 0, where 1 k < n, and show how the replacement of A by xA + yB, when k = 2, leads to a splitting of the characteristic curve, det(xA + yB zI) = 0, into lines and conics.

Mathematical Subject Classification 2000
Primary: 15A21
Milestones
Received: 15 March 1975
Published: 1 November 1975
Authors
Fergus John Gaines