A characterization for the nullity and rank of linear combinations of two idempotent matrices.
Abstract
In this article we will show in detail the equivalence between the nonsingularity of linear combinations of two idempotent matrices and nonsingularity of their sum. In addition we generalize the above said through nullity and rank of a matrix, and especially demonstrating that the nullity and rank of any nontrivial linear combination of two idempotent matrices is constant.
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