0
$\begingroup$

Suppose $B$ is an $N\times N$ matrix and $V$ is an $N\times 1$ vector.

I need to find a matrix representation for $V$:

$V_k = \sum_{j}B_{kj}^4 + 2\sum_{i\neq j}\sum_{j}B_{ki}^2B_{kj}^2$

Previously, I asked a somewhat similar question here: Need to find matrix formulation and I can't find the answer of this one either.

$\endgroup$
  • 2
    $\begingroup$ What do you mean by $B^4_{kj}$? Is it the components of the 4th power of the matrix $(B^4)_{kj}$, or the 4th power of the components of the matrix $(B_{kj})^4$? Are you multiplying matrices or numbers? $\endgroup$ – mr_e_man Sep 29 '18 at 14:14
  • $\begingroup$ 4th power of the components of matrix B $(B_{kj})^4$, I am multiplying numbers $\endgroup$ – farhadpti Sep 29 '18 at 19:35
0
$\begingroup$

For typing convenience, define $$A=\big(B\odot B\big)$$ where $\odot$ represents the elementwise/Hadamard product.

Then the vector can be written in matrix notation as $$\eqalign{ v &= (A\odot A)\,e + \big(2Ae\big)\odot\big(Ae-{\rm diag}(A)\big) \cr }$$ where $e$ is the vector whose elements are all equal to unity.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.