Hello, i am a little bit stuck with a formula that i need to figure out and code.

Picture is attached.
Original source http://www.beosil.com/download/MeshlessDeformations_SIG05.pdf

Apq = matrix(3x3)

m = is mass(float)

p = is position vector(x,y,z)

q = is transpose of position vector.

i need to calculate Apq.

what confuses me a little bit is that the output should be a matrix.

how should this matrix be assembled? as far as i know multiplication of vectors(p and q) will give me a float number , and not a matrix;

Thanks!

Do you know the outer product? The dot product is the inner product, which multiplies a 1*n matrix (row vector) with an n*1 matrix (column vector) and gives a 1*1 matrix (a scalar). The outer product multiplies a n*1 matrix with an 1*n matrix to obtain an n*n matrix. This is what you want here: p and q are column vectors (3*1) and their transpose is a row vector (1*3). Multiplying them together gives you a 3*3 matrix. You use the same rules as ordinary matrix multiplication to compute this outer product.

Reading: http://en.wikipedia.org/wiki/Outer_product