# Equalities for orthogonal projectors and their operations

Open Mathematics (2010)

- Volume: 8, Issue: 5, page 855-870
- ISSN: 2391-5455

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topYongge Tian. "Equalities for orthogonal projectors and their operations." Open Mathematics 8.5 (2010): 855-870. <http://eudml.org/doc/269712>.

@article{YonggeTian2010,

abstract = {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.},

author = {Yongge Tian},

journal = {Open Mathematics},

keywords = {Orthogonal projector; Idempotent matrix; Matrix equality; Rank equality; Range equality; Commutativity; Moore-Penrose inverse; Group inverse; Reverse-order law; orthogonal projector; idempotent matrix; matrix equality; rank equality; range equality; commutativity; group inverse; reverse-order law},

language = {eng},

number = {5},

pages = {855-870},

title = {Equalities for orthogonal projectors and their operations},

url = {http://eudml.org/doc/269712},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Yongge Tian

TI - Equalities for orthogonal projectors and their operations

JO - Open Mathematics

PY - 2010

VL - 8

IS - 5

SP - 855

EP - 870

AB - 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.

LA - eng

KW - Orthogonal projector; Idempotent matrix; Matrix equality; Rank equality; Range equality; Commutativity; Moore-Penrose inverse; Group inverse; Reverse-order law; orthogonal projector; idempotent matrix; matrix equality; rank equality; range equality; commutativity; group inverse; reverse-order law

UR - http://eudml.org/doc/269712

ER -

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