# Null space

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Null space of matrix $LaTeX: A.$ $LaTeX: \textstyle \left \{x: Ax=0 \right \}.$ It is the orthogonal complement of its row space, $LaTeX: \textstyle \left \{x: x=yA \mbox{ for some } y \in \mathbb{R}^m \right \}.$ Its dimension is $LaTeX: n - \mbox{rank}(A),$ which complements the subspace spanned by its row space.