# Tagged Questions

Questions on the manipulation of matrices in Mathematica.

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### Efficient solution of huge sparse linear system

I'm trying to improve efficiency of my code in which main task is a solution to huge (~$10^4\times 10^4$) but sparse linear system $$Ax=b$$ (In fact my aim is to solve nonlinear equations $F(x)=0$, ...
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### Bug in PositiveDefiniteMatrixQ?

Fixed in 10.1.0. Exists in at least 9.0.1 -- 10.0.2. This seems like a bug in PositiveDefiniteMatrixQ to me: ...
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### Why has Version 10.3 precision reduced?

In version 7.0.1.0 and versions 10.0 and 10.1 the following is produced: ...
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### Mapping over two indices with a condition

How can I use Map over two indices with a condition? I am trying to calculate second derivative of an eigenvalue, $\lambda_i(x)$, of $n \times n$ matrix $M(x)$ ...
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### Multivariate Path Construction using Sobol numbers

I am sharing my code,which I have tried to perform as per the instruction mentioned below. Please correct it so that I could get my output. Instruction: Use the first m dimensions of the Sobol vector ...
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### Speed matrix multiplications

I am trying to run this function ...
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### matrix multiplication performance

I would like to evaluate $$f(x,y)=\sum_{i=1}^{N} X_i(x)\,Y_i(y)$$ where $X_i(x)$ and $Y_i(y)$ are known functions for all $i=1,\ldots,N$, and $x$ and $y$ are from the rectangle $[0,A]\times[0,B]$, \$...
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### Getting an approximate analytical form for eigenvalues of a matrix

I have a 20x20 matrix: ...
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### Calculate the matrix M such M.X=omega

I would like to determine the matrix M[3,3] such as M.X=w. ...
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### Find algorithm or generator formula with automated procedure and pattern recognition

I am trying to find a generator formula for the discriminant of a polynomial and believe it would be an interesting problem for the Mathematica community to know how to automate evaluation of certain ...
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### How to find Pauli matrices

I wanted to find the Pauli matrices, so i wrote down this code: z = {{a, b}, {c, d}} i = {{1, 0}, {0, 1}} Solve[z.z == i, {a, b, c, d}] and mathematica gave me ...