Authors: Dodig, Marija 
Stošić, Marko 
Title: The general matrix pencil completion problem: A minimal case
Journal: SIAM Journal on Matrix Analysis and Applications
Volume: 40
Issue: 1
First page: 347
Last page: 369
Issue Date: 1-Jan-2019
Rank: M21
ISSN: 0895-4798
DOI: 10.1137/17M1155041
In this paper we resolve a classical, long-standing open general matrix pencil completion problem in a minimal case. The problem consists of describing the possible Kronecker invariants of a pencil with a prescribed subpencil, and the restriction we impose is not structural but is only on the number of added rows and columns. We completely resolve the problem in the case when the numbers of added rows and columns are the minimal possible, such that the resulting pencil can have the prescribed number of row and column minimal indices.
Keywords: Completion of matrix pencils | Majorization of partitions
Publisher: Society for Industrial and Applied Mathematics
Project: FCT project ISFL-1-1431
Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
Geometry, Education and Visualization With Applications 

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