# Questions tagged [linear-algebra]

Questions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.

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### System of linear equations where each equation is a symmetric matrix

I want to solve an underdetermined system of linear equations $A x = b$ with $A \in \mathbb{R}^{n \times r^2}, x \in \mathbb{R}^{r^2}, b \in \mathbb{R}^n$. The matrix $A$ has the following additional ...
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### Complexity of solving an image differential linear system

Define an "image differential linear system" as a linear system $A\mathbf{x}=\mathbf{b}$ wherein $\mathbf{x}$ contains the ($\mathbb{R}$) pixels of an image and each row of $A$ constrains ...
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### Parallelize Scipy iterative methods for linear equation systems(bicgstab) in Python

I need to solve linear equations system Ax = b, where A is a sparse CSR matrix with size 500 000 x 500 000. I'am using scipy.bicgstab and it takes almost 10min to solve this system on my PC and I need ...
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### Scientific calculator device malfunctioning [closed]

https://en.wikipedia.org/wiki/Scientific_calculator Can there be scenario/s that a scientific calculator gives incorrect answers in calculations to the end user?
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### How to make a directed graph symmetric?

Say I have a directed graph given as an adjacency matrix $A$ in CSR format represented by the arrays ia (row indexes) and ja (...
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### Equations that are easier to verify than to solve?

Are there interesting examples of (systems) of equations where it is known to be harder to find a solution (in terms of scaling with respect to problem size) than verifying a provided solution for ...
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### Range of a matrix from its complete orthogonal decomposition

In this StackOverflow answer, @Gokul has shown how to get a basis of the kernel of a matrix with the help of the 'Eigen' function CompleteOrthogonalDecomposition. ...
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### Trace of inverse from LU decomposition

Given an LU decomposition of $A\in \mathbb{R}^{n\times n}$, is there a way to compute $\operatorname{trace}(A^{-1})$ with lower complexity than that of the inversion ($O(n^3)$ in practice)? This ...
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### Formula for overdetermined logical matrix pseudoinverse not requiring SVD?

In https://commons.wikimedia.org/wiki/File:YI_%3D_PI.png, you will find a formula-based solution for an overdetermined logical matrix pseudoinverse. This simple formula gives the same result as the ...
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### A parallelized GMRES solver?

My application calls for solving a dense, 40,000 x 40,000, ill-conditioned linear system. The native SciPy GMRES solver with preconditioning has worked well for my application and solving a single ...