Definition:Row Space

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Let $R$ be a ring.

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

Let $\mathbf A^\intercal$ be 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 $\mathbf A^\intercal$.

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