Matrix Multiplication Python -- Memory Hungry
I'm not sure I completely follow exactly what processing you're doing to your data. The comments in the code suggest it's meant to be a matrix multiplication, the description you've provided above it suggests it's a cartesian product, but your code looks like does the sum of (flattened) outer products of corresponding rows. I'll proceed on the assumption that your code is doing the right thing, but hopefully you can clarify.

There are two general pieces of advice that apply here:


Separation of concerns. You're mingling code to parse your data with code to process it once it is parsed. Instead, parse everything into the appropriate data structures first, and then do the processing.
Use appropriate libraries and data structures. When you're doing linear algebra, that means numpy. Numpy is a dedicated, LA library that has heavily optimised routines for things like various matrix products, so you don't need to roll your own. Numpy arrays will also use quite a bit less memory than Python lists. However, what you're working with is labelled data (and some of it is labelled in two dimensions), which means the best data structure is probably a pandas dataframe - it's basically like your dict of strings to lists in pat_mRNA, but much more optimised, and fully compatible with numpy's matrix manipulations.


These things together will make your code easier to follow, more maintainable, and often both faster and shorter. 

So, start by looking at your core data structure:

exp_mat = [line.rstrip().split('\t') for line in ccle]


This is a list of lists of strings. For most of the rows, you don't seem to care about column 0 at all. Column 1 contains row labels, and corresponding to keys in your dictionary pat_mRNA. The rest of it is numeric data, currently stored as strings. It also contains 'header' rows - you only keep one of those around, so presumably you only expect one to be in there. I'm guessing that is column labels, which a DataFrame lets you include directly in the same data structure. 

The only trick parsing this into a DataFrame is that it is a little easier (and, apparently, more efficient) to swap the columns and rows from how you have them currently.  That will affect how it prints, and which methods you call to relabel things, but not much else. This is how I would parse it into a DataFrame:

data = pd.DataFrame()
headers = []
for line in ccle: 
    row = line.rstrip().split('\t')
    if row[0] == 'Name':
         headers = row
    elif row[1] in pat_mRNA:
        data[row[1]] = [float(f) for f in row[2:]]

if headers:
   data.index = headers


Note that I have modified your conditions a little, since yours seemed slightly off. The else branch of your condition effectively says "if the zeroth column is "name" or the first column isn't a match, it must be a header" - I've changed it so that instead, an appropriate value in the zeroth column is a header, and a non-matching first column on is ignored. 

I've maintained a temporary 'headers' list, because your code is currently robust against those appearing anywhere in the file. A better way to maintain that robustness would be if you know - or, preferably, can parse from your file before now - how many variables you have data for. Then you could do away with that headers list and do this:

data = pd.DataFrame(index=range(nvars))
for line in ccle: 
    row = line.rstrip().split('\t')
    if row[0] == 'Name':
         data.index = row
    elif row[1] in pat_mRNA:
        data[row[1]] = [float(f) for f in row[2:]]


In either case, I am assuming that you have one header for each variable. If that's a bad assumption, you may need to adjust this code.

As an aside, as a matter of commonly-accepted Python style (and in accordance with PEP 8), I have placed all of the code for each branch of the if in indented blocks, even if it is only one line. At most, you should only put it immediately after the : if there is only one branch to the if (no else or elifs), and even then, consider an indented block anyway.

I would change pat_mRNA to also be a DataFrame. You could change how you currently build it, or you could just pass the whole dictionary you have at the moment into pd.DataFrame(). 

Once you've done that, you can use numpy to do your LA work. As written, your entire strange product becomes this:

dot_prod_total = sum(np.outer(data[key], pat_mRNA[key]).flat for key in data)


Which should be quite a lot faster than trying to do it by list comprehensions, and may use multithreading depending on how numpy is compiled.