Definition:Row Space

Definition

Let $R$ be a ring.

Let $\mathbf A$ be a matrix over $R$.

Definition $1$

Let $\mathbf A^\intercal$ denote the transpose of $\mathbf A$.

Let the columns of $\mathbf A^\intercal$ be members of a vector space.

The row space of $\mathbf A$ is defined as the column space of $\mathbf A^\intercal$.

Definition $2$

The row space of $\mathbf A$ is defined as the vector space of all linear combinations of the rows of $\mathbf A$.

Also see

• Equivalence of Definitions of Row Space

• Definition:Column Space

• Definition:Left Null Space

• Results about row space can be found here.