# Questions tagged [linear-algebra]

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### Inverting a band matrix

I have a band matrix -- a sparse, square, symmetric $N \times N$ matrix whose structure looks like the following: Here, the area under the blue stripes is the non-zero elements; everything else is ...
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### Solving/Optimizing a linear system in a finite field (Z/2Z)

I'm trying to solve the following optimization problem. A is a rectangular matrix with coefficients in the finite field Z/2Z (size less than 1000 X 1000). I have a system of the form A.X = Y (X and Y ...
149 views

### Conditions for Linear Diophantine Equations to always have a solution

Given a set of $n$ linear equations in $v$ integer variables, where $v > n$, we can say that this system of equations will always have an integer solution. Over $\mathbb N$, is there any such ...
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### Can this system of polynomial equations be solved in polynomial time?

I have these $n$ equations, with $n$ variables. Variables are first $n$ positive integers, constants can be any rational number including zero. Given that there is always a solution, how do we find a ...
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### Absorbing Markov Chains: An efficient algorithmic approach

Following this procedure I have successfully written a program to calculate the probability of ending in a given absorbing state given the initial state. The procedure is as follows: Given the ...
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### Locality-sensitive hashing random projection

I'm trying to understand how the LSH works for Cosine Similarity metric. For instance, let's say you have $\vec{v} \in \mathbb{R}^d$ and the random vectors $\vec{r_{i}} \sim \mathcal{N}(0, 1)^d$ that ...
I'm trying to determine the exact complexity of finding an $n\times n$ matrix inverse of $A$. If it is known that the complexity of Gaussian elimination is $\frac{2}{3}n^3 + \frac{1}{2}n^2+O(n)$, then ...