The row space is the span over $\mathbb F$ of the rows of a matrix. Its dimension equals column rank. Over $\mathbb R$, identifying row vectors with their transposes gives $\operatorname{Row}(A)=\ker(A)^\perp$. Over $\mathbb C$, use $\operatorname{range}(A^*)$ for the corresponding Hermitian orthogonal complement; conjugation matters.
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