Rank of any submatrix of a Cauchy matrix

Asked Sep 14 '14 at 15:45

Active Jan 18 '20 at 13:43

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Here said that any $n \times n$ submatrix of a $m \times n$ cauchy matrix has full rank, where $m > n$.

Question: Is it possible to generalize the statement into non-sqaure submatrix? That is, any $a \times b$ submatrix of a cauchy matrix has full rank, where $a,b < m$

edited Jan 18 '20 at 13:43

Rodrigo de Azevedo

23,223

asked Sep 14 '14 at 15:45

Idonknow

16,493

1

Well, given that any submatrix of a Cauchy matrix is a Cauchy matrix … what do you think? – Harald Hanche-Olsen Sep 14 '14 at 16:32
I think it is possible to generalize the statement. But I don't know whether it is correct because I don't know how to prove it. – Idonknow Sep 14 '14 at 16:34
What I said is not restricted to square matrices. The statement you quoted implies that any Cauchy matrix has full rank. There isn't anything more to say. – Harald Hanche-Olsen Sep 14 '14 at 18:40

Rank of any submatrix of a Cauchy matrix

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