 Row and column spaces

The row space of a matrix is the span of its rows, and its column space is the span of its columns. Both have dimension equal to the matrix rank, though they lie in different ambient coordinate spaces for a rectangular matrix.

Row space and column space are fundamental concepts in linear algebra that are associated with matrices. They are used to understand the properties of linear transformations and the solutions of systems of linear equations. ### Row Space - **Definition**: The row space of a matrix is the vector space spanned by its rows. It consists of all possible linear combinations of the row vectors of the matrix.