Questions tagged [linear-algebra]
For challenges involving linear algebra, the mathematics of vector spaces and linear mappings between them.
57 questions
18
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7
answers
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Seven-dimensional cross product
The cross product is a peculiarly 3-dimensional phenomenon. There are multiple ways of generalizing it, but each of them have trade offs.
If you require that a cross product be a product of two ...
- 103k
14
votes
19
answers
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Antiparallel 12-hour Clock Hands
Output (or print) each of the 11 times, one per line, in the POSIX %I:%M:%S format, at which the hour and minute hands of a 12-hour clock are antiparallel. Here <...
- 811
12
votes
7
answers
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Contract a tensor
Introduction
Tensor contraction is an operation that can be performed on a tensor. It is a generalization of the idea of the trace of a matrix. For example, if we have a rank-2 tensor (a matrix) and ...
- 3,023
26
votes
41
answers
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Diagonalize a vector
Diagonalize a vector into a matrix.
Input
A vector, list, array, etc. of integers \$\mathbf{v}\$ of length \$n\$.
Output
A \$n \times n\$ matrix, 2D array, etc. \$A\$ such that for each element \$a_i \...
- 11.4k
15
votes
13
answers
1k
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Hankel transform of an integer sequence
A Hankel matrix is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.:
$$\begin{bmatrix} a & b & c & d \\ b & c & d & e \\ c & d &...
- 51.9k
7
votes
2
answers
525
views
NxM List Combination Closest to Target
Given a list of N lists, each containing M positive integers, and a separate list of M positive integers (target values), return a list of N scalars (integers with a value of 0 or more) that ...
- 757
15
votes
7
answers
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Are these the basis vectors?
A basis of a vector space \$V\$ is a set of vectors \$B\$ such that every vector \$\vec v \in V\$ can be uniquely written as a linear combination of the vectors in \$B\$. In other words, let \$B = \{\...
- 50.9k
16
votes
4
answers
801
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Bad matrix multiplication that gives the right answer
Executive summary:
Print NxN matrices \$A\$ and \$B\$ where \$ AB = 10A + B \$. Largest N wins!
Details:
Entrants in this challenge should choose an N. Submit a program that takes an input integer '...
- 1,153
17
votes
10
answers
1k
views
Decomposition of a matrix in \$ SL_2(\mathbb{Z}) \$
Background
The special linear group \$ SL_2(\mathbb{Z}) \$ is a multiplicative group of \$ 2 \times 2 \$ matrices whose elements are integers and determinant is 1.
It is known that every member of \$...
- 79.3k
6
votes
6
answers
652
views
Explore a Klarner-Rado sequence [duplicate]
One of the Klarner-Rado sequences is defined as follows:
the first term is \$1\$
for all subsequent terms, the following rule applies: if \$x\$ is present, so are \$2x+1\$ and \$3x+1\$
the sequence ...
- 173
29
votes
8
answers
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Billiard balls collision
Given the 2-dimensional positions and velocities of a pair of billiard balls right before impact, calculate their velocities after a perfectly elastic collision. The balls are assumed to be ideal ...
- 15.6k
24
votes
18
answers
5k
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Find the inverse of a 3 by 3 matrix
Challenge
Given nine numbers, a, b, c, d, e, f, g, h, i, as input which correspond to the square matrix:
$$\mathbf{M} = \begin{pmatrix}a& b& c\\ d& e&...
- 23.6k
13
votes
9
answers
3k
views
Calculate the Hafnian as quickly as possible
The challenge is to write the fastest code possible for computing the Hafnian of a matrix.
The Hafnian of a symmetric 2n-by-2n ...
user9206
31
votes
10
answers
1k
views
Find the dot product of Rationals
I was at a friend's house for dinner and they suggested the idea of a "Prime-factor vector space". In this space the positive integers are expressed as a vector such that the nth element in the ...
- 103k
14
votes
13
answers
3k
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Characteristic polynomial
The characteristic polynomial of a square matrix \$A\$ is defined as the polynomial \$p_A(x) = \det(Ix-A)\$ where \$I\$ is the identity matrix and \$\det\$ the determinant. Note that this definition ...
- 17k
12
votes
5
answers
852
views
Solve a matrix equation by Jacobi's method (Revised)
Mathematical Background
Let A be an N by N matrix of real numbers, b a vector of N real numbers and x a vector N unknown real numbers. A matrix equation is Ax = b.
Jacobi's method is as follows: ...
- 229
22
votes
14
answers
2k
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Is the matrix rank-one?
Given a matrix of integers, test if it's rank-one, meaning that every row is a multiple of the same vector. For example, in
...
- 150k
27
votes
10
answers
4k
views
Symbolic matrix multiplication
There are lots of different ways to explain matrix multiplication. I'll stick with a single figure since I believe most people here are familiar with it (and the figure is very descriptive). If you ...
- 46.8k
15
votes
3
answers
518
views
Totally Invertible Submatrices
(inspired by this question over on Math)
The Definitions
Given an n x n square matrix A, we can call it invertible if there ...
- 43.7k
10
votes
14
answers
832
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Dot Product of Diagonals
This challenge is very simple. You are given as input a square matrix, represented in any sane way, and you have to output the dot product of the diagonals of the matrix.
The diagonals in specific are ...
- 25.8k
20
votes
5
answers
1k
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Jordan Decomposition
Important note: Because this challenge only applies to square matrices, any time I use the term matrix, it is assumed that I am referring to a square matrix. I am leaving off the “square” description ...
user45941
13
votes
11
answers
2k
views
Calculate the Kronecker Product
Related, but very different.
In the examples below, \$A\$ and \$B\$ will be \$2\times2\$ matrices, and the matrices are one-indexed.
A Kronecker product has the following properties:
...
- 46.8k
9
votes
6
answers
1k
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Calculate the Kronecker sum of two matrices
In the examples below, A and B will be 2-by-2 matrices, and the matrices are one-indexed.
A Kronecker product has the ...
- 46.8k
13
votes
6
answers
2k
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Solve a Linear Equation
This challenge but with a better spec.
Spec
Your program will take a linear equation containing a single variable x and output the value of ...
- 29.2k
18
votes
12
answers
1k
views
Recursive 2x2 determinant
The determinant of a 2 by 2 matrix
a b
c d
is given by ad - bc.
Given a matrix of digits with dimensions 2n by 2n, n ≥ 1, ...
- 62.2k