Using the elements of one Matrix to form a new Matrix with specified rules

Given a matrix [a], how to get matrices [b] and [c] based on the following two rules?

  1. rule [a]->[b]: Strike out corresponding term in [a] and take product of the remaining two terms in the same column.
  2. rule [a]->[c]: Strike out the row and column containing the corresponding term in [a] and take sum of cross products in the 2×2 matrix remaining.

x,y,z can be replaced with 1,2,3; For example, $ a_{xy},a_{yz}$ can be replaced with a12,a23; [a] can be replace with:

a = {{a11, a12, a13}, {a21, a22, a23}, {a31, a32, a33}} 

Thank you

Matrix [a]

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Matrix [b]

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Matrix [c]

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How do I input a 2d matrix when no spacing is given in adjacent elements while taking the input in c++?

Thanks for looking over, so I’m trying to take a nxn matrix as input where in the input is in the following format example :

4 1123 3442 5632 2444 

you see the input format that’s my problem I don’t want those elements to be stuck together and c++ is reading the rows as if each of the row is a number which means “cin” is reading only n elements and I expect it to read all n×n elements to be read separately. Pardon me if the question wasn’t upto the mark as this is my first question.

Selecting k rows and k columns from a matrix to maximize the sum of the k^2 elements

Suppose $ A$ is an $ n \times n$ matrix, and $ k \ge 1$ is an integer. We want to find $ k$ distinct indices from $ \{1, 2, \ldots, n\}$ , denoted as $ i_1, \ldots, i_k$ , such that

$ \sum_{p, q = 1}^k A_{i_p, i_q}$

is maximized. In words, we seek $ k$ rows and the corresponding $ k$ columns, such that the intersected $ k^2$ elements of $ A$ have the largest sum.

This problem can be formulated as a quadratic assignment problem, which is NP-hard and admits no polynomial time algorithm with constant approximation bound. I’m just wondering if for this specific problem (as a special case of quadratic assignment), there exists a poly-time algorithm with constant approximation bound. Thank you.

Finding largest sum of $k$ elements below threshold

I was working on a project and am stuck in the middle unable to find an optimal method to solve this problem. Consider an array $ A$ of $ n$ elements. I have to choose $ k$ elements such that the sum of indices is maximal under the constraint of being less than a given element $ x$ . My approach for this is the naive $ O(n^k)$ algorithm, but this would take a lot of time for large $ n$ .

This is isn’t a homework problem.

dynamically create elements on button click

I’m using create guten blocks to create a custom block for my theme and I need to create a list item with an onClick.

<script> function addItem() {   var ul = document.getElementById("ul-item");   var li = document.createElement("li");   var input = document.createElement("input");   input.type = "text";   li.setAttribute("id", "li-item");   li.appendChild(input);   ul.appendChild(li); } </script>  <ul id='ul-item'>   <li id="li-item"><input type="text" value="" /></li> </ul> <button onClick='addItem()'>Add Item</button> 

see the fiddle

something like that I just don’t know how to do it in CGB and can’t find anything using google.

Prove that if you pair arbitrarily pair up the elements of an array A of size n to get n/2 pairs,

then you discard pairs of unequal elements and keep just one from the pairs of matching elements. Then the resulting collection will have a majority if and only if A had a majority, i.e. there exists an element with more than floor(n/2) occurrences.

I am very confused about how to go about proving this. It is from a textbook DPV problem 2.23. I am trying to prove it but I end up disproving it.

I.e. Suppose we have an array of n elements A[], that has a majority of element x. that means A.count(x) > floor(n/2). Now suppose that if we add two different elements, [a, b] to array A, x is no longer the majority. Then: A.count(x) <= floor(n/2) + 1 -> A.count(x) = floor(n/2) + 1. But now if we apply the same procedure and pair [a, b] together, then by definition the resulting array should have a majority, even though the original [….] o [a, b] did not.

Pick out elements from a list of lists using criteria

Consider a list of lists in this form (with a shape $ m \times n \times 3 $ ):

{  {{a1, R1, c11}, {a2, R1, c12}, {a3, R1, c13}, ..., {an, R1, c1n}},  {{a1, R2, c21}, {a2, R2, c22}, {a3, R2, c23}, ..., {an, R2, c2n}},  ...,  {{a1, Rm, cm1}, {a2, Rm, cm2}, {a3, Rm, cm3}, ..., {an, Rm, cmn}} } 

where in each outer list, the 2nd element $ R_i $ is fixed ($ i = 1, 2, …, m $ ), and the 1st element changes from $ a_1 $ to $ a_n $ , the 3rd element $ c_{ij} $ is normally a complex and its imaginary part can change from positive to negative or from negative to positive for several times. Here is a sample data for test.

I want to pick out the neighbor lists whenever the imaginary part of $ c_{ij} $ changes its sign, say, for $ R_2 $ , the selected lists are something like $ \{a_j, R_2, c_{2j}\} $ and $ \{a_{j+1}, R_2, c_{2,j+1}\} $ , where $ \text{Im} c_{2,j} < 0 $ and $ \text{Im} c_{2,j+1} > 0 $ . More generally, for $ R_p $ I pick out $ \{a_j, R_p, c_{pj}\} $ and $ \{a_{j+1}, R_p, c_{p,j+1}\} $ , and then to plot a curve with ListLinePlot[{{R1, a01}, {R2, a02}, ..., {Rp, a0p}, ..., {Rm, a0m}}], in which $ a_{0j} = (a_j + a_{j+1}) / 2 $ . In other words, I what to plot a parameter curve w.r.t the 1st and 2nd elements, across which the imaginary part of the 3rd element changes sign.

I tried Cases, Select and ParametricPlot, but I am still having trouble to find all the pairs of the neighboring lists when the imaginary part of $ c_{ij} $ changes its sign.