It is stated in almost every linear algebra text i could find that the inverse of a triangular matrix is also triangular, but no proofs accompanied such statements.(adsbygoogle = window.adsbygoogle || []).push({});

I am convinced that it is the truth, but I have not been able to write anything down that I am satisfied with that doesnt rely on the argument that row operations on the matrix (A|I) to obtain (I|A^{-1}).

Since this would only be the forward pass(if A is lower triangular) and the backwards pass(if A is upper triangular) and these operations ultimately do not introduce non zero terms above/below the diagonal entries(depending on what A was), thus A^{-1} would be a triangular matrix of the same flavor.

Has anyone come across anything a little more elegant than simply brute forcing it?

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

Dismiss Notice

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!

# Triangular matrices

Loading...

Similar Threads - Triangular matrices | Date |
---|---|

I Triangular Matrix RIngs ... Lam, Proposition 1.17 | Sep 18, 2016 |

I Triangular Matrix RIngs ... Another Question | Sep 17, 2016 |

I Example on Triangular Rings - Lam, Example 1.14 | Sep 15, 2016 |

Simple showing inverse of matrix also upper triangular | Nov 11, 2015 |

Some clarification on upper triangular matrices please. | Dec 18, 2004 |

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