# [Solved] How to compute cosine similarity using two matrices

I have two matrices, A (dimensions M x N) and B (N x P). In fact, they are collections of vectors – row vectors in A, column vectors in B. I want to get cosine similarity scores for every pair `a`

and `b`

, where `a`

is a vector (row) from matrix A and `b`

is a vector (column) from matrix B.

I have started by multiplying the matrices, which results in matrix `C`

(dimensions M x P).

C = A*B

However, to obtain cosine similarity scores, I need to divide each value `C(i,j)`

by the norm of the two corresponding vectors. Could you suggest the easiest way to do this in Matlab?

##
Solution #1:

The simplest solution would be computing the norms first using element-wise multiplication and summation along the desired dimensions:

```
normA = sqrt(sum(A .^ 2, 2));
normB = sqrt(sum(B .^ 2, 1));
```

`normA`

and `normB`

are now a column vector and row vector, respectively. To divide corresponding elements in `A * B`

by `normA`

and `normB`

, use `bsxfun`

like so:

```
C = bsxfun(@rdivide, bsxfun(@rdivide, A * B, normA), normB);
```