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Submatrices with the best-bounded inverses: Studying mathds{R}^(n times 2) and mathds{C}^(n times 2)
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Submatrices with the best-bounded inverses: Studying mathds{R}^(n times 2) and mathds{C}^(n times 2)
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In both real and complex cases, we establish the connection of the problem about $2$-dimensional linear subspaces the most deviating from the coordinate ones with one simply formulated optimization problem for isoperimetric polygons in Euclidean spaces. This study thereby provides a new geometrical point of view on the $2$-dimensional case of the problem formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997}, and at the same time presents a new application of the results by Hausmann and Knutson \cite{HK1997}.
Forward citations
Cited by 3 Pith papers
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Submatrices with the best-bounded inverses: an asymptotically tight upper bound for $\mathbb{C}^{n \times 2}$
Proves an asymptotically tight upper bound on the spectral norm of the best-bounded-inverse 2x2 submatrix for arbitrary complex n x 2 orthonormal-column matrices.
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On the submatrices with the best-bounded inverses
For k=2 and any n, every n x 2 orthonormal matrix U has a 2 x 2 submatrix Q with smallest singular value at least 1/sqrt(n).
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Submatrices with the best-bounded inverses: the equality criterion for $\mathbb{R}^{n \times 2}$
The equality criterion for submatrices with the best-bounded inverses is established for real n by 2 matrices.
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