Completion of an orthogonal projector and a related inverse mapping problem

We study the completion problem for an orthogonal projector A of R n from knowledge of one or several of its columns, as well as the related matrix inverse problem of finding an orthogonal projector A with AX = Y for two given n by k matrices X and Y. Using geometric properties of orthogonal project...

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Bibliographic Details
Published in:Linear algebra and its applications 2005-07, Vol.403, p.229-247
Main Authors: Meng, Chunjun, Hu, Xiyan, Zhang, Lei, Uhlig, Frank
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Inverse problem
Linear and multilinear algebra, matrix theory
Mathematics
Matrix completion
Orthogonal projector
Orthonormal basis
Sciences and techniques of general use
Singular-value decomposition
Subspace
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Summary:We study the completion problem for an orthogonal projector A of R n from knowledge of one or several of its columns, as well as the related matrix inverse problem of finding an orthogonal projector A with AX = Y for two given n by k matrices X and Y. Using geometric properties of orthogonal projections and of the singular value decomposition, we derive theoretical and numerical solutions for these problems. We give algorithms and test their MATLAB implementations.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2005.02.008