1. So I'm having trouble understanding the max notation and exactly what it means.

I have a problem I'm working and this is what it is saying

What is the interpretation of this in english, I understand this much.

L1 norm of A = to the max of ||Ax|| when ||x|| = 1 , but what is a good way of thinking about it.
d
I've also seen the notation used with arg max, I assume they are the same. I'm just having a hard time understanding the interpretation of this.

2.

3. The notation is used for any norm, not just L1. I presume you know what A and x mean in this context. ||x|| is the norm of a vector x. Consider the subset consisting of all vectors in the space with ||x||=1, and then all the images (Ax) of these vectors under the operator A. max||Ax|| of these is the norm of A.

The third term (max j) looks screwed up.

4. A is a matrix or transformation and x is a vector. Their image is another vector.

So the l1 norm of a vector would then be column that gives the maximum l1 norm.

For instance:

A = (1 2; 3 4)

L1 norm of A = 2 + 4 = 6 ?

Is that a correct assumption? To say that the norm would be sum of the column with the largest values? since the norm of x is 1 we are selecting the largest column.

5. I haven't examined it in detail, but it looks OK so far. Have you looked at cases where the matrix elements are some positive and some negative?

I think you need to look at the max j term - it seems to have typos.

6. Originally Posted by GenerationE
I think I fixed it, the j term wasn't supposed to be multiplied. I have it right on paper, I just entered in incorrectly on here.

I expanded this to the infinity norm of A and I got that the the Infinity norm of a matrix is the sum of the row with the largest values. It's interesting that these appear to be inverses of each other. I'm now working on the L2 norm or a matrix but it's much more difficult than the other two.

7. It still doesn't look right, the sum is over j and you have max over j outside the sum. Should it be max over i?

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