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
Canonical name	OntoLinearTransformationDefinitionOf
Date of creation	2013-03-22 15:25:30
Last modified on	2013-03-22 15:25:30
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	7
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 03-00