Definition:Full Rank

Definition

Let $K$ be a field.

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

$\mathbf A$ is said to be of full rank if and only if its rank equals the minimum of $m$ and $n$.

Also known as

The rank of a matrix can also be referred to as:

its row rank

its column 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: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rank: 3. (of a matrix)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rank: 3. (of a matrix)