1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to prove the product of upper triangular matrices is upper triangular?

  1. Jan 12, 2015 #1
    This seems easy but when I tried to do this, the best way I came up with is to list all entries and then do the multiplication work. Is there any better ,clearer and more simple way to do the proof?
     
  2. jcsd
  3. Jan 12, 2015 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Did you try to express the entries in the product matrix in terms of the dot products of the row of one matrix with the corresponding column in the second matrix?
     
  4. Jan 12, 2015 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Suppose A is an upper triangular matrix with elements ##a_{ij}##. Then you know that ##a_{ij}=0## if ##i>j##. If C=AB where B is also upper triangular, you want to show that ##c_{ij}=0## if ##i>j##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How to prove the product of upper triangular matrices is upper triangular?
  1. Triangular matrix (Replies: 0)

Loading...