Matrix Completion Problems

Cravo, Glória

doi:10.1016/j.laa.2008.12.029

Cited by 21 publications

(13 citation statements)

References 53 publications

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“…Instead, it is only the single quantity, the singularity degree, that drives this regularity concept. For any feasible X, the constraint X 22 = 0 forces 0 = X 12 = X 33 . By an inductive argument, then we deduce X 1k = 0 and X k,k = 0 for all k = 2, .…”

Section: Singularity Degree and The Hölder Error Bound In Sdpmentioning

confidence: 99%

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The Many Faces of Degeneracy in Conic Optimization

Wolkowicz

2017

FNT in Optimization

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Section: Singularity Degree and The Hölder Error Bound In Sdpmentioning

confidence: 99%

“…Surveys for matrix completion are given in e.g., [70,68,4,63,32,33,71,69]. A survey specifically related to chordality is given in [139].…”

Section: Commentarymentioning

confidence: 99%

The Many Faces of Degeneracy in Conic Optimization

Wolkowicz

2017

FNT in Optimization

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“…Further suppose U is a 2 × 2 matrix which satisfies (1) such that t = Tr(U ). Then (6) det(U ) = Tr(U ).…”

Section: Remarks 1) the System Has The Trivial Solutionmentioning

confidence: 99%

“…Throughout the last decades, numerous results have been published in the area of the so-called Matrix Completion Problems (see [1] for a recent survey).…”

Section: Introductionmentioning

confidence: 99%

Some matrix completions over integral domains

Călugăreanu

2016

Linear Algebra and its Applications

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“…On the other hand, rectangular matrices arise in many contexts in linear control theory and matrix completion problems and are also of considerable interest. We refer to Cravo [1,Thms. 15,32] for specific examples of matrix completion problems.…”

Section: Introductionmentioning

confidence: 99%

The number of linear transformations defined on a subspace with given invariant factors

Ram

2017

Linear Algebra and its Applications

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Given a finite-dimensional vector space V over the finite field F q and a subspace W of V , we consider the problem of counting linear transformations T : W → V which have prescribed invariant factors. The case W = V is a well-studied problem that is essentially equivalent to counting the number of square matrices over F q in a conjugacy class and an explicit formula is known in this case. On the other hand, the case of general W is also an interesting problem and there hasn't been substantive progress in this case for over two decades, barring a special case where all the invariant factors of T are of degree zero. We extend this result to the case of arbitrary W by giving an explicit counting formula. As an application of our results, we give new proofs of some recent enumerative results in linear control theory and derive an extension of the Gerstenhaber-Reiner formula for the number of square matrices over F q with given characteristic polynomial.

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Matrix Completion Problems

Cited by 21 publications

References 53 publications

The Many Faces of Degeneracy in Conic Optimization

The Many Faces of Degeneracy in Conic Optimization

Some matrix completions over integral domains

The number of linear transformations defined on a subspace with given invariant factors

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