How to create a matrix from product of all elements in two arrays?

Question

I was reading the documentation for matlab on element-wise multiplication and I came across this example:

Create a row vector a and a column vector b, then multiply them. The 1-by-3 row vector and 6-by-1 column vector combine to produce a 6-by-3 matrix with all combinations of elements multiplied.

The documentation sure showed the output, but how did they get to that output matrix of size6,3? Which was obtained from multiplying a column vector b of size 6,1, and a row vector a of size 1,3 using the methods explained in the document.

Answer 1

This is called broadcasting. When one dimension is 1 while the other is bigger, the unit dimension is expanded, as if with repmat:

 6 1 : column
 1 3 : row
 ------
 6 3 : result

Given

a = 1:3
b = [1:6]'
a .* b

is roughly equivalent to

a2 = repmat(a, 6, 1)
b2 = repmat(b, 1, 3)
a2 .* b2

But of course broadcasting is much more memory efficient.