# Finding Gram Matrix

Matrix manipulation by hand is often times pain in the neck when it comes to anything bigger than 2 by 2 matrices as it involves a quite amount of arithmetic operations. Well, I’ve got an Intel Core 2 Duo processor and Python. No reason not to take advantage of them ;-)

### Source Code

```
__author__ = 'Sumin Byeon <sumin@cs.arizona.edu>'
from Numeric import *
# u and v are lists of same lengths
def inner_product(u, v):
return reduce(int.__add__, map(lambda x: x[0]*x[1], zip(u, v)))
# vs: a list of vectors
def gram_matrix(*vs):
n = len(vs)
mx = zeros((n, n))
for i in range(0, n):
for j in range(0, n):
mx[i,j] = inner_product(vs[i], vs[j])
return mx
```

### Result

```
>>> gram_matrix([1,0,0,1], [-2,1,0,0], [-1,0,-1,0], [0,2,-3,0])
[[ 2 -2 -1 0]
[-2 5 2 2]
[-1 2 2 3]
[ 0 2 3 13]]
```