Definition:Rank/Matrix/Definition 1
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Definition
Let $K$ be a field.
Let $\mathbf A$ be an $m \times n$ matrix over $K$.
Then the rank of $\mathbf A$, denoted $\map \rho {\mathbf A}$, is the dimension of the subspace of $K^m$ generated by the columns of $\mathbf A$.
That is, it is the dimension of the column space 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
- Results about the rank of a matrix can be found here.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices