On linear combinations of two tripotent, idempotent, and involutive matrices. (English) Zbl 1165.15022

Sarduvan, Murat; Özdemir, Halim

Appl. Math. Comput. 200, No. 1, 401-406 (2008).

Let (1) \(A = c_{1}A_{1} + c_{2}A_{2}\), where \(c_{1}, c_{2}\) are nonzero complex numbers, and (\(A_1, A_2\)) is a pair of two \(n\times n\) nonzero matrices. The purpose of this paper is mainly twofold: in case \(A_1\) and \(A_2\) are involutive matrices, to characterize all situations where a linear combination of the form (1) is a tripotent or an idempotent or an involutive matrix, then to determine all situations where a linear combination of the form (1) is an involutive matrix when \(A_1\) and \(A_2\) are tripotent or idempotent matrices.

Reviewer: Yueh-er Kuo (Knoxville)

MSC:

15B57

Hermitian, skew-Hermitian, and related matrices

Keywords:

involutive matrix; idempotent matrix; tripotent matrix; diagonalization; quadratic form

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