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definition of onto linear transformation

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

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

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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Cross-references: one-to-one, transformation, solution, homogeneous, spans, iff, onto, linear transformation

This is version 4 of definition of onto linear transformation, born on 2005-07-26, modified 2006-10-29.
Object id is 7270, canonical name is AlternativeOntoLinearTransformation.
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03-00 (Mathematical logic and foundations :: General reference works )

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