If V is a vector space with an inner space <.,.>. V1 is an non empty subset of V. Vector x is contained in V is said to be orthogonal to v1 if <x,y>=0 for all y contained in V1.(adsbygoogle = window.adsbygoogle || []).push({});

1) if v is contained in V and define the mapping f(x)=<x,v>v. Show f is a linear transformation and describe its range and kernel.

2) if v1 is a subspace of V show that V1 and direct sum of V1 (orthogonal) = V.

I tried to prove these as they were stated in a website. But failed. PLease kindly assist me on this matter.

Thank.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mapping ( linear transformation)

Loading...

Similar Threads - Mapping linear transformation | Date |
---|---|

I Does this theorem need that Ker{F}=0? | May 1, 2017 |

I Difference between 'Field' (algebra) and 'Field' (geometry) | Mar 1, 2016 |

Proof of invertibility | Feb 4, 2016 |

Non linear maps | Jul 9, 2015 |

Adjoint of an adjoint of a linear map | Jan 12, 2015 |

**Physics Forums - The Fusion of Science and Community**