Tagged Questions

54 views

Order of group $GL_{2}\left( \mathbb{F}_{p}\right)$

I'm having a hard time counting. I need to count the number of elements for the multiplicative group of invertible $2\times 2$ matrices $GL_{2}\left( \mathbb{F}_{p}\right)$ with elements from the ...
44 views

54 views

How many nonnegative integer matrices of size $N$ have all row and column sums equal to $D$?

Given the positive integer $N$ and $D$, generate all the non-negative integer matrices which satisfy matrix dimension is $N\times N$; sum of each row elements equals to $D$ sum of each column ...
62 views

Rearrange columns and rows of a matrix such that it can be split in half

I am not a mathematician, so please excuse me if this question turns out to be trivial. I need this at work, but I could not figure out how to solve this efficiently, though it looks like it might be ...
186 views

How to distribute 5-digit numbers in 5x5 matrices

I have 98000 5-digit numbers, from 00001 to 98000. I need to distribute these 98000 numbers in 14000 5x5 matrices. A matrix cell must contain only a digit from 0 to 9. Each matrix must receive 7 ...
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Sum of $\mathbf{x}\mathbf{x}'\mathbf{x}\mathbf{x}'$ when $\mathbf{x}$ is a binary vector of length $n$

Let's say $\mathbf{x}$ is an $n\times 1$ column vector where each entry can be either 1 or -1. There can be $2^n$ possibilities for this vector. Let $\mathbf{x}'$ be a transpose of $\mathbf{x}$. I ...
31 views

Transform a symmetric matrix to a vector and multiplicate

Assume that we have a matrix symmetric matrix $A = \mathbb{R}^{nxn}$. It es enough to look only at the lower triangle. What I want to do is to transform the matrix into a vector: \begin{pmatrix} 1 ...
Given the size of a matrix is $N \times N$, how many unique matrices are there given the following restrictions: Matrix entries can only contain numbers $\left[0,b\right]$ A valid matrix cannot have ...