How to write this equation in matrix form?

Question

If I have a $n\times n$ matrix $A$ and a column vector $v$ of $n$ elements, I would like to define vector $x$ as:

$$x_{i} = \sqrt{\sum_{j}^{n}(A_{ij}v_{j})^{2}}$$

How can I write this in matrix form?

Is this ok, where $\circ$ is the Hadamard product?

$$x = \sqrt{A(v \circ v)}$$

I don't think you can write it in matrix form without using some external tools, because the equation is not linear. — TZakrevskiy, Jul 26 '13 at 08:59

score 1 · Answer 1 · answered Jul 26 '13 at 08:55

1

You can write this as below:$$x\circ x=(A\circ A)(v\circ v)$$

answered Jul 26 '13 at 08:55

I thought something else when I wrote first. Now I've edited my answer. – Samrat Mukhopadhyay Jul 26 '13 at 09:00
Why is the down vote? – Samrat Mukhopadhyay Jul 26 '13 at 09:08
Your previous answer was incorrect. The edited version is correct though. – Raskolnikov Jul 26 '13 at 09:29
yes, I wrote the previous answer mistakenly, and found the error as soon as I posted. Now I've edited it. – Samrat Mukhopadhyay Jul 26 '13 at 09:31

score 1 · Accepted Answer · answered Jul 26 '13 at 08:58

1

Rather $\sqrt{(A\circ A)(v\circ v)}$, where $\sqrt{\bullet}$ is a “Hadamard (i.e., element-wise) square root.”

answered Jul 26 '13 at 08:58

triple_sec

2 Answers2