# Questions tagged [matrix]

Matrix is a rectangular array of elements (e.q. numbers, symbols, or expressions), arranged in columns and rows.

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### When does reduced integration lead to artificial zero energy modes in stiffness matrix?

This question relates to the topic of locking free finite element development. In the case of application of reduced integration to global stiffness matrix for the Timoshenko beam element with ...
308 views

### Fastest Way to Mutiply $10^4$ 2x2 Matrices

In a code that I work with (written in python, but also tagging as matlab because numpy is so close and I could use it if need be), we use a transfer matrix method to compute the properties of a ...
245 views

### Polynomial rooting - fast root finding

I need to solve a rooting problem of a polynomial (the order of which is 2(N-1), where N=48). So far I'm using Python Numpy algorithm (that relies on computing the eigenvalues of the companion matrix)...
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### Comparing Two Matrix Notation

I have two matrix A and B, I want to find pattern B in matrix A. So I get 2 pattern similar like pattern B. What the name of this operation? and How I write this in mathematics notation? Thank you in ...
2k views

### Efficient ways to numerically evaluate matrix exponentials

What are some computationally efficient ways to solve matrix exponentials, i.e. functions of the form : $f(X)=e^{X}$, where $X$ is a square matrix? So far I have been able to diagonalise some ...
632 views

### Inverting really big symmetric block diagonal matrix

I have a really big symmetric 7.000.000 X 7.000.000 matrix that i would like to invert. The matrix is extremely sparse and it can be rearranged as to become a block diagonal matrix. The biggest blocks ...
12k views

### why is A*v+B*v faster than (A+B)*v?

$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,...
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### How to know which LAPACK's function is used by Scipy's eig function?

As far as I understood, scipy.linalg.eig use wrappers from scipy.lapack to compute the eigenvalues and eigenvectors of a matrix. ...
346 views

### Fastest way to calculate the $2$-norm (or an upper bound for the $2$-norm) of the inverse of a matrix $A\in \mathbb{C}^{N\times N}$

I have a matrix $A\in \mathbb{C}^{N\times N}$ and I need to calculate $||A^{-1}||_{2}$ efficiently. Can it be done without having to evaluate the inverse explicitly? In general, I am looking for ...
218 views

### Numerical stability in the product of many matrices

I have to calculate in numpy the matrix-product of many matrices (~400). Are there common practices to increase numerical stability? If this is relevant, the matrices are $300\times 300$ orthogonal ...
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### Find index for submatrix with maximum sum

Given an N-dimensional matrix A, I want to find an M<N dimensional index array I such ...
178 views

### What is the fastest algorithm for computing log determinant of a PSD matrix? (All possible PSD matrices)

I am diving into some literature to understand which is the best algorithm for computing the log-determinant of a PSD matrix. More generally, I am interested in a list of resources to read, which ...
149 views

### Calculate Transformation Matrix between two sensors

My question is if I can calculate the transformation matrix between two sensors. Each sensor provides a $4\times 4$ matrix for every timestep recorded. The sensors are moving and have some noise in ...
415 views

### Does a symmetric positive definite matrix also have $\mathbf{A} = \mathbf{L}^T\mathbf{L}$ (where $\mathbf{L}$ is a lower triangular matrix)?

As we know, for a symmetric positive definite (SPD) matrix $\mathbf{A}$, there is a theorem about the Cholesky factorization $\mathbf{A}= \mathbf{L}\mathbf{L}^T$, where $\mathbf{L}$ is a lower ...
290 views

### How to compute all the eigenvalues of a large sparse matrix using matlab?

In matlab, there are 2 commands named "eig" for full matrices and "eigs" for sparse matrices to compute eigenvalues of a matrix. And eig(A) computes all the eigenvalues of a full matrix and eigs(A) ...
295 views

### Recursive Algorithm to Calculate Determinant via Expansion of Minors in C#

I have been recently trying to attempt to write an algorithm in C# that would calculate the determinant of a matrix via recursion using the expansion of minors method. I understand that there are ...
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### implementation for coppersmith matrix multiplication

Is there any online implementation for the coppersmith matrix multiplication I have searched alot but can not find any? and if there is not any why is that Isn't this algotithm much faster than ...
299 views

### What algorithm do BLAS and ATLAS use for matrix multiplication?

I have searched and what I understood was that they use the naive one with several memory and cache optimizations. However, I wanted to know whether they are using the Strassen or the Coppersmith-...
674 views