Equalities for orthogonal projectors and their operations
نویسنده
چکیده
A complex square matrix A is called an orthogonal projector if A2 = 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. MSC: 15A03, 15A09, 15A27, 15B57
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تاریخ انتشار 2010