Abstract
Here we study properties of the unique Green completion obtained in Theorem 8.2 of the previous Chapter 8. In the first section it is shown that this completion is invertible if and only if all the matrices \(D_{k}=\tilde{A}(k-n:k,k-n:k),\qquad k=n+1,....,N\) are invertible. In this case all the principal leading submatrices \(A^{(j,k)}=A(j:k,j:k),\quad 1\leq j <j+n\leq k\leq N\) of the completion are also invertible.
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© 2014 Springer Basel
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Eidelman, Y., Gohberg, I., Haimovici, I. (2014). Completion to Matrices with Band Inverses and with Minimal Ranks. In: Separable Type Representations of Matrices and Fast Algorithms. Operator Theory: Advances and Applications, vol 234. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0606-0_9
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DOI: https://doi.org/10.1007/978-3-0348-0606-0_9
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0605-3
Online ISBN: 978-3-0348-0606-0
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