Definition:Rank/Matrix/Definition 2

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

• Equivalence of Definitions of Rank of Matrix

• 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