# onto linear transformation, definition of

The linear transformation $T:\mathbb{R}^{n}\to\mathbb{R}^{m}$:

$\displaystyle T(\mathbf{x})=A\mathbf{x}$

is onto iff $\operatorname{Col}A$ spans $\mathbb{R}^{m}$. However, if the corresponding homogeneous system has only the trivial solution, the transformation is one-to-one.

Title onto linear transformation, definition of OntoLinearTransformationDefinitionOf 2013-03-22 15:25:30 2013-03-22 15:25:30 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Definition msc 03-00