Equalities for orthogonal projectors and their operations

• Autorzy: Yongge Tian
• Języki publikacji: EN

Abstrakty

EN

A complex square matrix A is called an orthogonal projector if A 2 = A = A*, where A* denotes the conjugate transpose of A. In this paper, we give a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. We first collect some well-known rank formulas for orthogonal projectors and their operations, and then establish various new rank formulas for matrix expressions composed by orthogonal projectors. As applications, we derive necessary and sufficient conditions for various equalities for orthogonal projectors and their operations to hold.

Słowa kluczowe

EN

Orthogonal projector; Idempotent matrix; Matrix equality; Rank equality; Range equality; Commutativity; Moore-Penrose inverse; Group inverse; Reverse-order law

Kategorie tematyczne

• 15A27: Commutativity
• 15B57: Hermitian, skew-Hermitian, and related matrices
• 15A03: Vector spaces, linear dependence, rank

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 5
• Strony: 855-870

Daty

wydano

2010-10-01

online

2010-09-28

Twórcy

autor

Yongge Tian

• Central University of Finance and Economics

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0057-9