Definition:Rank/Matrix/Definition 3

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Let $K$ be a field.

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

The rank of $\mathbf A$, denoted $\map \rho {\mathbf A}$ is the largest number of elements in a linearly independent set of rows of $\mathbf A$.

Also known as

The rank of a matrix can also be referred to as its row rank.

Some sources denote the rank of a matrix $\mathbf A$ as:

$\map {\mathrm {rk} } {\mathbf A}$

Also see

  • Results about the rank of a matrix can be found here.