# paper about linear independence in altered Vandermonde and Cauchy Matrices

Both Vandermonde and Cauchy matrices with $n$ rows and $k$ ($n \geq k$) columns have the property that any $k$ rows are linearly independent (assuming the coefficient are independent). It seems to me that if you concatenates the rows of the identity matrix $I_k$ then the $k$-linear independence is preserved in the resulting ($k+n$ x $k$) matrix.

I want to use this claim in a paper and I want to know if there is already a formal work that I can cite to back up my (supposed true) claim. Otherwise I will do it in the annex section and post it here too.

thanks

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At least in the Vandermonde case, you are (implicitly) assuming that the nodes are all distinct, yes? Otherwise you have (obvious) linear dependence... –  Guess who it is. May 2 '12 at 18:47
yes I make this implicit assumption. –  UmNyobe May 2 '12 at 18:49
If by "add up" you mean that you want to concatenate the matrices into a single matrix, changing the wording might make the statement a little clearer. –  rschwieb May 2 '12 at 19:20