Definition:Rank/Matrix

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Definition

Let $K$ be a field.

Let $\mathbf A$ be an $m \times n$ matrix over $K$.


Then the rank of $\mathbf A$, denoted $\rho \left({\mathbf A}\right)$, is the dimension of the subspace of $K^m$ generated by the columns of $\mathbf A$.


That is, it is the dimension of the column space of $\mathbf A$.


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