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I found this. What is it?

  1. Feb 11, 2012 #1
    So I found this on the ground before I took my ACT this morning:


    It doesn't appear to be very difficult, but I don't really know what it is. It's probably pretty simple, I just don't recognize it.

    If anyone could tell me what this represents, or what type of classes it might be associated with, that would be great!

    (Also: If you're Josh Carison, I don't know who you are, but I think I may have found your homework)
  2. jcsd
  3. Feb 11, 2012 #2


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    That is linear algebra.
  4. Feb 11, 2012 #3
    So, It really is just vectors and matrices? I thought maybe there was something else to it. Hrm. Ok then.
  5. Feb 11, 2012 #4
    While vectors and matrices are an important part of linear algebra, they are far from representative of the whole subject. Linear algebra deals primarily with vector spaces, which are sets with addition and scalar multiplication satisfying certain axioms (regular vectors in Euclidean space also fall under this definition). A function T:V→W (where V and W are vector spaces) is called a linear transformation if T(u+v)=T(u)+T(v) and T(cv)=cT(v) for all u and v in V and all scalars c.

    With the choice of a basis for a vector space V (a set of vectors which acts like a "coordinate system"), the elements of V can be written as lists and linear transformations from V to itself can be written as (square) matrices. Thus matrices are important in linear algebra, but ultimately just represent linear transformations in a particular basis (which makes calculations more convenient).
  6. Feb 11, 2012 #5
    That's quite helpful! Thanks!
  7. Feb 11, 2012 #6
    I don't like people to fall into the "matrix trap" (to get the impression that linear algebra is nothing more than solving systems of linear equations with matrices, etc). Matrices don't do the subject justice.
  8. Feb 11, 2012 #7
    Since the original purpose of this thread has been fulfilled, I think it's ok to go ahead and go off-topic for a bit.

    I'm pretty sure Keanu Reeves is in the "Matrix Trap".
  9. Feb 12, 2012 #8


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    indeed, matrices stop being a useful way to think about linear transformations when we have non-finite bases.

    still, it IS profitable to think of Rn with respect to the standard basis, and using standard bases for Rn,Rm allows us to easily compute the values of a linear transformation T:Rn→Rm using an mxn matrix.

    and studying matrices does give one a "feel" for the ways in which an "abstract" linear transformation behaves. and often, in physical applications, one has certain "coordinate systems" in mind, from the outset, and one is looking for some numerical quantity which expresses something we are measuring in these coordinate systems (like, say, a force vector).

    p.s.: i don't think the use of "matrix" in the famed movie series has anything to do with linear algebra, but rather is the broader english meaning of "an inter-connected web"

    (matrix: < L. matrix, "expectant mother" < L. mater, "mother"....later "origin/source" or "place of development", and then (c. 17-th century) "embedding/enclosing mass").
  10. Feb 12, 2012 #9
  11. Feb 15, 2012 #10
    By the way if you ever run into Josh Carison you could tell him that in addition to using very very sloppy notation he made some errors in his homework.
  12. Feb 15, 2012 #11
    Yeah, I assume that's why he cast it so hastily aside!

    Thanks for the discussion everyone!
  13. Feb 16, 2012 #12
    Matrices for doing, linear maps for understanding.
  14. Feb 16, 2012 #13
    Well said.
  15. Feb 16, 2012 #14
    Indeed. Good work out of you.
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