On Idempotency of Linear Combinations of Two 2×2 Idempotent Matrices

Notes on linear combinations of two tripotent , idempotent , and involutive matrices that commute

The aim of this paper is to provide alternate proofs of all the results of our previous paper [2] in the particular case when the given two matrices A1 and A2 in the linear combination A = c1A1 + c2A2 commute.

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.

The Group Involutory Matrix of the Combinations of Two Idempotent Matrices

On Nonsingularity of Linear Combinations of Tripotent Matrices

Let T1 and T2 be two commuting n × n tripotent matrices and c1, c2 two nonzero complex numbers. The problem of when a linear combination of the form T = c1T1 + c2T2 is nonsingular is considered. Some other nonsingularitytype relationships for tripotent matrices are also established. Moreover, a statistical interpretation of the results is pointed out.

Ela on the Group Inverse of Linear Combinations of Two Group Invertible Matrices

hold. If such matrix X exists, then it is unique, denoted by A, and called the group inverse of A. It is well known that the group inverse of a square matrix A exists if and only if rank(A) = rank(A) (see, for example, [1, Section 4.4] for details). Clearly, not every matrix is group invertible. It is straightforward to prove that A is group invertible if and only if A is group invertible, and ...