In linear algebra, nonsquare matrices serve as operators that map vectors between vector spaces of different dimensions while preserving linearity through parallel grid preservation and origin mapping to the origin. The geometric interpretation is defined such that a matrix's row dimension corresponds to the coordinate space of the output (codomain), whereas its column dimension represents the basis size of the input space (domain). This mechanism establishes that full rank nonsquare matrices transform an n-dimensional subspace into either m > n dimensions via embedding or onto k < n dimensional subspaces like planes or lines, without necessarily being invertible.
In linear algebra, nonsquare matrices serve as operators that map vectors between vector spaces of different dimensions while preserving linearity through parallel grid preservation and origin mappin…