# Of vector and matrix products

Listed below are definitions of some vector or matrix products. I will be needing these definitions in the succeeding posts. Thanks to Jetpack‘s Latex support, I can now include equations in my post.

### Outer Product

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:

### Kronecker Product

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.

### Khatri-Rao Product

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:

and

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?