Definition:Rank/Matrix/Definition 3

Definition

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

• 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)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rank (of a matrix)