MATLAB: How to perform norm on each row of a matrix

Question

I have a matrix and each row of the matrix is a vector. I want to perform norm function on each row of this matrix and save the result in a new matrix.

For example, if I had these vectors:

u = [-1 1 0; -1 1 0]
v = [0 1 1; 0 1 -1]

I wanted to calculate the angle between the vectors of the corresponding rows. So the answer should look like this:

angle = [60 ; 60]

But whatever I tried has not worked:

angle = atan2d(norm(cross(u,v,2)),dot(u,v,2))

works for single vectors, but not for a matrix of vectors. This is because I cannot perform the norm function on each row of the two matrices. I also tried this:

angle = atan2d(normr(cross(u,v,2)),dot(u,v,2))

but did not work.

How can I get a result like this:

n = [norm of vectors of first row ; norm of vectors of second row ; norm of vectors of third row ; ...]

witout using a loop?

Answer 1

What is a norm? I assume by norm, you mean the common Euclidean norm, thus the 2-norm. (Other norms will be just as easy for the most part.)

Could you just use a loop? Of course. But why?

Can you take square all of the elements of your matrix? (I hope so.)

Then it should be easy to sum them, along each row.

Finally, what will the sqrt of that result be? (Hint: the norm that you want.)

In fact, the above will be doable in a fully vectorized form, at least if you did what I suggested.

sqrt(sum(X.^2,2))

When you don't know how to solve a problem, then break it down. Figure out how to solve each component part of the probem. And when all else fails, just use a brute force loop. But expect it to be slow and clumsy, at least loop solution would be so here. But it would trivially work.