Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

I know this may sound so "newbieish", but I really need some clarification. While resaerching over the net I came across a proof on a derivation of the Matrix p-norms. While reading, I stumbled upon this part of the proof:

[tex]

\| Ax \|_1 \leq \sum^n_{i=1} \left| \sum^n_{k=1} a_{ik}x_k \right| = \left( \sum^n_{k=1} |x_k| \right) \left( \sum^n_{i=1} |a_{ik}| \right)

\quad (1)

[/tex]

I am confused when I came upon this. I know that

[tex]

\left( \sum_j a_j \right) \left(\sum_k b_k\right) = \sum_j \sum_k a_j b_k \quad (2)

[/tex]

But in (1), the [tex]b_k[/tex] term is given by [tex]a_{ik}[/tex]. Is it possible to "split" the two summation symbols into a product of two sums even though it's clear that [tex]a_{ik}[/tex] is dependent on both i and k?

All help is appreciated

Thanks,

Reli~

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Clarification on the Summation symbol

**Physics Forums | Science Articles, Homework Help, Discussion**