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# 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.

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## Mathematics Subject Classification

03-00*no label found*

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