If a set of vectors in R^n (or C^n) contains more than n elements

Created almost 9 years ago, updated about 8 hours ago

Any list of more than $n$ vectors in $\mathbb F^n$ is dependent. Its column matrix has more columns than possible pivots, so the homogeneous system has a free variable. This is a dimension bound; exactly $n$ vectors may be either independent or dependent.

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