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Math 23a: Proof 9.1

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Xuất bản 28/06/2016
Math 23a: Proof 9.1 by Raviv Murciano-Goroff: Let W be an open subset of Rn+m, and let F:U→Rn be a C1 mapping such that F(c)=0. Assume that [DF(c)] is onto. Prove that the n + m variables can be ordered so that the first n columns of [DF(c)] are linearly independent, and that [DF(c)] = [A|B] where A is an invertible n × n matrix.
math proof