Criterion for linear independence of functions

Abstract

Using a generalization of forward elimination, it is proved that functions $f_1,...,f_n:X\to \mathbb{A}$, where $\mathbb{A}$ is a field, are linearly independent if and only if there exists a nonsingular matrix $[f_i(x_j)]$ of size $n$, where $x_1,...,x_n\in X$.

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