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!

Homework Help: Describe all vectors orthogonal to col(A) with a twist

  1. Nov 3, 2015 #1
    I am trying to solve the following problem:

    Let A be a real mxn matrix. Describe the set of all vectors in F^m orthogonal to Col(A).

    Here, F^m could be C^m. Now in the real case, I'd say that the column space of A is the row space of A^T, and it is well known that the row space of a matrix is orthogonal to it's null space ---> Col(a) is orthogonal to Null(A^T) (left nullspace). After significant research, I can't see how to change/adapt this statement for the complex field. Any help is greatly appreciated.

  2. jcsd
  3. Nov 3, 2015 #2


    User Avatar
    Homework Helper

    I don't think much changes when you move to the complex numbers, or any field in general.
    If some real vectors ##\{R^m\} ## are orthogonal to the columns of a purely real A, then the imaginary vectors ##\{i R^m\} ## will also be orthogonal since it is a scalar multiple of an orthogonal vector.
    So, then you essentially should have any linear combination of those real and imaginary vectors.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted