Of vector and matrix products
Given a row vector with n elements and another vector with m elements, the outer product of u and v is given by
The outer product as defined above can also be written as a matrix multiplication:
Given two matrices A which is m-by-n and B, which is q-by-p, the Kronecker product C of A and B is given by:
where C is an mp-by-nq matrix.
Using the above definition, we can now define the Khatri-Rao product C of two matrices A and B as a column-wise Kronecker product of the two matrices. First, rewrite the matrices A and B as follows:
where represent the columns of A and B, respectively. The Khatri-Rao product is given by
Whew! I thought including equations was easy. Just hover your mouse over the equations above and you’ll see how complicated the code is to write such simple equations. There should be a better way. Anyone?