I'm preparing for an end of year linear algebra test which briefly covers things about subsets of Matnxn and their relations to subspaces of Matnxn; I found the following question:(adsbygoogle = window.adsbygoogle || []).push({});

Which of the following subsets of Matn×n are subspaces of Matn×n?

(i) Symmetric matrices (i.e. matrices A such that AT = A).

(ii) Skew-symmetric matrices (i.e. matrices A such that AT = −A).

(iii) Orthogonal matrices (i.e. matrices A such that AT = A−1).

(iv) Singular matrices.

(v) Invertible matrices.

(vi) Echelon matrices.

(vii) Reduced echelon matrices.

----

I'd appreciate some guidance on how to tell which of the above apply.. is it the same as showing that vectors in a subset are subspaces when they're closed under addition and linear multiplication?

thanks.

**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!

# Some subspace questions

Loading...

Similar Threads for subspace questions | Date |
---|---|

General Question on Subspaces | May 10, 2014 |

Shilov's Linear Algebra Subspace Question | Mar 7, 2014 |

Question on subspaces and spans of vector spaces | Apr 17, 2012 |

Question about projections and subspaces | Aug 19, 2011 |

Subspace question | Jun 3, 2010 |

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