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!

I Linear Transformation notation

  1. Mar 1, 2016 #1
    I'm confused about the notation
    T:R^n \implies R^m
    specifically about m. From my understanding if n=2 then (x1, x2). Are we transforming n=2 to another value m for example (x1, x2, x3)?
  2. jcsd
  3. Mar 1, 2016 #2


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    That is very possible. It is easy to define linear transformations that go from Rn into a subspace of Rm, where m can be smaller, equal, or greater than n:

    m smaller than n: (x1, x2) => x1
    m equals n: (x1, x2) => (-x1, x1+x2)
    m greater than n: (x1, x2) => (x1, x2, x1+x2); another is (x1, x2) => (x1, 0, 0)
  4. Mar 1, 2016 #3


    Staff: Mentor

    That's not the way to think about it. T isn't transforming a single number, like n. It's a map between a space of n dimensions to another space of m dimensions. If n = 2 and m = 3, T is a map from vectors in the plane to vectors in space (three dimensions).

    Ordinary functions, which you're probably more familiar with, are maps from ##\mathbb{R}^1## to ##\mathbb{R}^1##. (I added the 1 exponents only for emphasis.) A function of two variables is a map from ##\mathbb{R}^2## to ##\mathbb{R}^1##.
  5. Mar 1, 2016 #4
    Okay makes sense. We're transforming vectors.
    I don't feel confident with my understanding of this statement. What does it mean from vectors in the plane
  6. Mar 1, 2016 #5


    Staff: Mentor

    Two-dimensional vectors, like <2, -1>. A vector in space would be, for example, <3, 1, 2>.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted