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Math Help - Can i do this with a matrix multiplication operator

  1. #1
    Newbie
    Joined
    Aug 2005
    From
    'straya
    Posts
    18

    Question Can i do this with a matrix multiplication operator

    Letís say I want to find a vector of possible revenues, where revenue equals Price times quantity:
    R=P*Q
    P and Q are vectors of length N, say for this example, N=2, and i want a vector N=2 for R

    P=(a,b)' and Q=(c,d)' (both column vectors, dimension 2*1).
    A simple vector multiplication (where Q is transposed R=P*Q') yields a scalar:
    R=(ac+bd)

    A simple vector multiplication (where P is transposed R=P'Q) yields a 2*2 matrix:
    R=
    (ac,ad)
    (bc,bd)

    What I actually want is the (2*1) vector as a "product" of the P and Q vector:
    R=
    (ac)
    (bd)
    Is there a "product" operator that will do this?


    If I set up P and Q as N*N matrices (instead of N vectors) with values on the diagonals:
    P*=
    (a 0)
    (0 b)
    Q*=
    (c 0)
    (0 d)
    Then P*Q yields:
    R*=
    (ac)
    (bd)

    This gives me the elements I want, but I want them in a vector, not a matrix.

    I'm fresh out of ideas...

    Update:
    Yes i can turn
    R*=
    (ac 0)
    (0 bd)
    into
    R=
    (ac)
    (bd)
    by multiplying R* by the column vector:
    (1)
    (1)

    but this doesn't help put the column vectors P and Q into diagonal matrices P* and Q*. I don't think any operation can do that, can it?

    I am almost about to define my own matrix operation that does what i want it to nice and neatly. It will be called:
    Farmer's Vector Multiplication.
    Look for it in a math forum near you!
    Last edited by TheFarmer42; August 16th 2005 at 06:34 PM.
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  2. #2
    Newbie
    Joined
    Aug 2005
    From
    'straya
    Posts
    18
    In the end i've sort of cheated, i mean simplified, by using element by element multiplication by defining the problem in terms of arrays rather than matrices.
    Everyone's a winner.
    TF
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