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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The equality criterion for submatrices with the best-bounded inverses is established for real n by 2 matrices.
k-subspaces from scaled star spaces of series-parallel graphs achieve the conjectured maximum deviation arccos(1/sqrt(n)) from coordinate subspaces, with uniqueness of the weighting.
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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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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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About subspaces the most deviating from the coordinate ones
k-subspaces from scaled star spaces of series-parallel graphs achieve the conjectured maximum deviation arccos(1/sqrt(n)) from coordinate subspaces, with uniqueness of the weighting.