There are two types of matrix or vector multiplication: “dot product” style and “elementwise”. These are fundamentally different mathematical operations. What we are always doing here is taking a mathematical formula and translating it into python code. So that requires that you first understand what the math says and then understand the functionality provided by the numpy calls you have at your disposal. Note that you need to have a good understanding of basic Linear Algebra as a prerequisite here. You don’t need to know what an eigenvalue is, but you definitely need to be comfortable with how dot product matrix multiply works.
So what is going on with the cost formula? The fundamental operation there is taking two 1 x m vectors, computing the products of the corresponding elements and then adding up those products. There are (at least) two ways I can think of to do that using numpy vector operations:
- Use
np.multiplyor * (elementwise multiply) and then usenp.sumto add up the products. - You can do both operations in one shot with
np.dotto compute the dot product of the two vectors.
But note that in the dot product case, just dotting 1 x m with 1 x m does not make sense, right? So what do you need to do to make that work? If you’re not familiar with the rules for dot products, then you really should spend some time learning the basics of Linear Algebra first before continuing here. That is pretty fundamental and we’re only just getting rolling here: it doesn’t get easier or less complicated as we proceed through the courses here.
Here’s a thread which discusses the general issues in a bit more detail.