Hi!(adsbygoogle = window.adsbygoogle || []).push({});

I am working on the following problem:

If a matrix is antisymmetric (thus A^T = -A), show that

P = {A [tex]\in[/tex] R | A is antisymmetric} is a subset of Rnxn. Also, find the dimension of P.

So far, I've proven that P is a subset of R and I am guessing that, in order for me to find the dimension, I need to find the basis of P first. Here is where I am kind of stuck.

I understand what the properties of the base would be (1. the vectors inside the set will be linearly independent and 2. the basis will be a spanning set for P), but how exactly should I start working so that I can find the basis itself...

A hint would be highly appreciated!

Thanks a bunch guys!

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

Join Physics Forums Today!

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

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

# A problem with basis and dimension

Loading...

Similar Threads - problem basis dimension | Date |
---|---|

Least Square basic problem | Jan 20, 2018 |

A Eigenvalue Problem and the Calculus of Variations | Jan 8, 2018 |

Difficult theoretical problem on basis vectors | Mar 26, 2012 |

A problem on finding orthogonal basis and projection | Nov 21, 2011 |

A problem on linear transformation and standard basis | Oct 24, 2011 |

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