The sum of involutory matrices - Pelejo, Diane Christine P. (2011)
Let K be a commutative ring with unity. An n-by-n matrix A, with entries in K,is said to be an involution if A2 = In. If A2= -In, we say that A is a skew-involution. For K=C,R,Q,Z and Zk, this paper determines the necessary and sufficient conditions for an n-by-n matrix to be expressible as a sum of involutions. The number of involutory summands for complex matrices satisfying these conditions is investigated. This study also classifies all complex matrices that can be written as a sum of two involutions. For matrices with entries from Z2, we classify all companion matrices that is a sum of two involutions. Analogous facts are established for the sum of skew-involutions.
"October 2011."
Thesis (M.A. Mathematics)--University of the Philippines Diliman.
Keywords: Matrices