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Linear Algebra

  1. Nov 21, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img136.imageshack.us/img136/8452/linalg.png [Broken]


    2. Relevant equations

    I'm trying to figure out what it's asking me to do, as soon as I figure that out, I maybe be able to figure out the equation...

    We've gone over stuff like finding the Vector OQ(->) on something like this..
    http://img24.imageshack.us/img24/8452/linalg.png [Broken]

    Anybody have a clue what it's asking?

    I've seen equations like;
    ||a|| = sqrt ( ATA)

    and

    http://img689.imageshack.us/img689/8452/linalg.png [Broken]

    and some others.. Thanks
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 22, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The "column space" of matrix A is the subspace spanned by its columns. One way to find the projection of a vector on a subspace is:

    Construct a basis for the subspace.
    Add vectors to extend to a basis for the entire space.
    Write your given vector in that basis.

    Drop the terms involving basis vectors not in the subspace.

    In this case, if the columns themselves are independent vectors, you can use the column vectors as your basis for the subspace.
     
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