Letís say I want to find a vector of possible revenues, where revenue equals Price times quantity:R=P*QP 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:
A simple vector multiplication (where P is transposed R=P'Q) yields a 2*2 matrix:
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:
This gives me the elements I want, but I want them in a vector, not a matrix.
I'm fresh out of ideas...
Yes i can turn
R*=(ac 0)(0 bd)into
R=(ac)(bd)by multiplying R* by the column vector:
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!