What is the rule on the preservation of rank through an elementary operation? I know that rank can never go up, but is there any direct way to determine that it goes down (either than reducing the matrix down to row-echelon form)? Is there a good source that go into the proofs for properties of rank like this?(adsbygoogle = window.adsbygoogle || []).push({});

A side question is is it possible to have a linear dependency on rows as well as columns, or is the whole notion of such a dependency moot as both types are fungible?

Thanks

**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!

# I Elementary operations & rank

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Elementary operations rank | Date |
---|---|

B Proof of elementary row matrix operation. | Jun 6, 2017 |

I Intuition behind elementary operations on matrices | May 20, 2017 |

Elementary Row Operations and Preserving Solutions. | Mar 13, 2011 |

Inverse of a Matrix M as a Product of Elementary Row Operations. Uniqueness? | Mar 11, 2011 |

Elementary Row Operations - only need two? | Jan 19, 2009 |

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