Definition:Rank/Matrix/Definition 2
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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