Eigenvalues of functions of orthogonal projectors
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چکیده
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An approach is proposed which, given a family of linearly independent functions, constructs the appropriate bi-orthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves iteratively and it is endowed with the following properties: i) it yields the desired bi-orthogonal functions avoiding the need of inverse operations ii) it allows...
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Sudipto Banerjee ([email protected]) received his B.S. in Statistics from the University of Calcutta, India, an M.Stat. from the Indian Statistical Institute, Calcutta, and then his M.S. and Ph.D. from the University of Connecticut, Storrs. He is currently an Assistant Professor in the University of Minnesota, Minneapolis, where his research interests include spatial statistics and model...
متن کاملEqualities for orthogonal projectors and their operations
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 v...
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Representing two orthogonal projectors on a finite dimensional vector spaces (i.e., Hermitian idempotent matrices) as partitioned matrices turns out to be very powerful tool in considering properties of such a pair. The usefulness of this representation is discussed and several new characterizations of a pair of orthogonal projectors are provided, with particular attention paid to the spectral ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2009
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.07.023