# Definition:Rank/Matrix/Definition 2

< Definition:Rank | Matrix

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## Definition

Let $K$ be a field.

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

Let $\mathbf A$ be converted to echelon form $\mathbf B$.

Let $\mathbf B$ have exactly $k$ non-zero rows.

Then the **rank** of $\mathbf A$, denoted $\map \rho {\mathbf A}$, is $k$.

## 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.

## Sources

- 1998: Richard Kaye and Robert Wilson:
*Linear Algebra*... (previous) ... (next): Part $\text I$: Matrices and vector spaces: $1$ Matrices: $1.5$ Row and column operations