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

1. Can i do this with a matrix multiplication operator

Let’s 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=
(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!

2. 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