Comprehensive classification of the algebra generated by two idempotent matrices
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Date
2025
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Publisher
Elsevier Inc.
Abstract
For two idempotent matrix P,Q?Cn×n, let alg(I<inf>n</inf>,P,Q) denote the smallest subalgebra of Cn×n that contains P,Q and the identity matrix I<inf>n</inf>. This paper provides a complete classification of alg(I<inf>n</inf>,P,Q) without imposing any restrictions on P and Q. As a result of this classification, the issue of group invertibility within alg(I<inf>n</inf>,P,Q) is fully resolved. © 2024 Elsevier Inc.
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Keywords
Complete classification, Finite-dimensional algebras, Group inversion, Idempotent matrix, Identity matrices, Invertibility, Matrix P, Subalgebras, Two projection
Citation
Linear Algebra and Its Applications, 2025, 705, , pp. 185-206