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

Composition of Linear Transformation and Matrix Multiplication2

  1. Mar 18, 2009 #1
    Theorem 2.12: Let A be an mxn matrix, B and C be nxp matrices, and D and E b qxm matrices. Then
    (d.) If V is an n-dimensional vector space with an ordered basis B, then [IV]B = In.

    My question: What does [IV]B mean? Is this the identity matrix with respect to the vector space V which is with respect to the basis B-I'm not sure what that means. Could someone explain this in as much detail possible.


  2. jcsd
  3. Mar 19, 2009 #2


    User Avatar
    Science Advisor

    Yes, that is exactly what it means. Specifically, it is saying that if IV(x)= x is the "identity" linear transformation on vector space V, then it is represented by the same matrix no matter what basis you use and that matrix is the n by n matrix with "1"s down then main diagonal and "0"s everywhere else, In.

    (Surely, "Let A be an mxn matrix, B and C be nxp matrices, and D and E b qxm matrices" relates to something else. There is no "A", "C", "D" or "E" in what you give and B is NOT a matrix.)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook