Fractional Minimal Rank

Ben W. Grossmann; Hugo J. Woerdeman

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arXiv · 1710.07343

Fractional Minimal Rank

Ben W. Grossmann·Hugo J. Woerdeman

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Abstract

The notion of fractional minimal rank of a partial matrix is introduced, a quantity that lies between the triangular minimal rank and the minimal rank of a partial matrix. The fractional minimal rank of partial matrices whose bipartite graph is a minimal cycle are determined. Along the way, we determine the minimal rank of a partial block matrix with invertible given entries that lie on a minimal cycle. Some open questions are stated.

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Ben W. Grossmann, Hugo J. Woerdeman. 2017-10-19. Fractional Minimal Rank. https://arxiv.org/abs/1710.07343

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