# onto linear transformation, definition of

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

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

is onto iff $\mathrm{Col}A$ 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 |
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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 |