Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

About singular matrices

  1. Aug 18, 2011 #1
    Just a small question, I think I may have missed this part out in our lectures or something. :|

    Suppose I have a singular matrix A; will there always exist another matrix B such that AB (/BA) will be the zero matrix?
     
  2. jcsd
  3. Aug 18, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Yes, take B the zero matrix :smile: but you mean non-zero matrices, I suppose.

    Well, if A is singular, then there always exists a nonzero column vector x such that Ax=0. Then B=(x x ... x) should do the trick.
     
  4. Aug 18, 2011 #3

    I like Serena

    User Avatar
    Homework Helper

    Welcome to PF ohyeahstar! :smile:

    Yep, as mm said!

    More specifically, a matrix has a so called "null space" (or "kernel space") and a so called "column space" (or "image" or "range" of the matrix).
    Any matrix with columns selected from the null space will satisfy your criterion for B.
    Furthermore the columns from your matrix A "span" the column space.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: About singular matrices
  1. Singular Matrices (Replies: 12)

Loading...