Questions tagged [matrix]
This tag is for challenges involving matrices. A matrix, also known as a 2D array, is a list of numbers arranged in a rectangle with rows and columns.
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Create Bernard from Desmos
Background
In the online graphing calculator Desmos, there is a certain shape that appears in the lower left portion of the graph in many high detail graphs, which the Desmos community has dubbed &...
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Matrix with 1 to L(n), in all n columns
Challenge:
Take a list, L containing positive integers as input:
3 5 2 1 6
and create a matrix where the n'th column contains the vector 1:L(n), where shorter ...
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Generate this number table
Given an integer \$1 < n < 10 \$ generate a table like below.
For \$n = 5\$,
1 2 3 4 5
2 2 3 4 5
3 3 3 4 5
4 4 4 4 5
5 5 5 5 5
For \$n = 8\$,
...
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Find the submatrix with the smallest mean
You're given a n-by-m matrix of integers, where n,m > 3. Your task is to find the 3-by-3 sub-matrix that has the lowest mean, and output this value.
Rules and clarifications:
The integers will be ...
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Sorting rectangular matrices
Given a matrix A, we can say that it is "sorted" if each row and column of A is sorted (ascending left-to-right for ...
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Count the contiguous submatrices
Migrated from chat
Given two non-empty non-negative integer matrices A and B, answer the number of times A occurs as a contiguous, possibly overlapping, submatrix in B.
Examples/Rules
0. There may not ...
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Index of the row with most non-zero elements
This is a simple one: Take a matrix of integers as input, and output the index of the row with the most non-zero elements. You may assume that there will only be one row with the most non-zero ...
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Rebuild a rectangular array from a corner
I once had a beautiful rectangular array. It was very symmetrical, but unfortunately it has fallen apart and now I only have the top left corner. Your task will be to rebuild the original array.
Your ...
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Orthodiagonal steps
It's a common problem to navigate in a 2D matrix. We've seen it many times and will see again. So let's help future us and develop the shortest solutions to generate all eight possible steps in a 2D ...
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Create a checkerboard matrix
Take a positive integer n as input, and output a n-by-n checkerboard matrix consisting of 1 and 0.
The top left digit should always be 1.
Test cases:
...
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Is it a stochastic matrix?
A stochastic matrix is a matrix of probabilities used in the context of Markov chains.
A right stochastic matrix is a matrix where each row sums to 1.
A left ...
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Generate all square sub-matrices of a given size
You will be given a square matrix of integers M and another positive integer n, strictly smaller than the size of M. Your task is to generate all square sub-matrices of M of size n.
For the purposes ...
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Turn this array into a matrix
Take a non-nested array as input. Turn it into a matrix by using the following method:
Let's say my array is [1, 2, 3, 4, 5]
First, I repeat that array 5 times: (...
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Construct the Identity Matrix
The challenge is very simple. Given an integer input n, output the n x n identity matrix. The identity matrix is one that has <...
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Check if all non-zero elements in a matrix are connected
Input:
A matrix containing integers in the range [0 - 9].
Challenge:
Determine if all non-zero elements are connected to each other vertically and/or horizontally.
Output:
A truthy value if all ...
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Do Matrix Multiplication!
In mathematics, matrix multiplication or the matrix product is a binary operation that produces a matrix from two matrices. The definition is motivated by linear equations and linear transformations ...
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Hilbert-Curvify a Matrix
Inspired by this question
Another way to unroll a 2D image into a 1D string is to use an Hilbert Curve.
There are many version of this curve, depending on the number of iterations used while ...
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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 ...
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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 \...
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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
...
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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 ...
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Zigzagify a Matrix
As part of its compression algorithm, the JPEG standard unrolls a matrix into a vector along antidiagonals of alternating direction:
Your task is to take a matrix (not necessarily square) and return ...
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4D rotation matrix to quaternions
It is well-known that a 3D rotation can always be represented by a quaternion. It is less well-known that a 4D rotation can always be represented by two quaternions, sending a point \$p=(a,b,c,d)^T\$ ...
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Matrix Trigonometry
Introduction
The two most common trigonometric functions, sine and cosine (or sin and ...
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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 ...
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Odd'em out: letters
Objective
Write a program or function (or equivalent) that sorts out and returns the odd letter in the matrix of random size.
Details
You will be passed a matrix (as a string) as input of random ...
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22
answers
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Compute this fractal matrix
The unique-disjointness matrix ( UDISJ(n) ) is a matrix on all pairs of subsets of {1...,n} with entries $$ U_{(A,B)}=\begin{cases}
0, ~ if ~ |A\cap B|=1\\
1, ~ ...
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5
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Compute the logarithm of a matrix
There have already been challenges about computing the exponential of a matrix , as well as computing the natural logarithm
of a number. This challenge is about finding the (natural) logarithm of ...
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11
votes
6
answers
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Calculate the Smith normal form of an integer matrix
Given an \$m \times n\$ matrix of integers A, there exist a \$m \times m\$ matrix P, an \$m \times n\$ matrix D, and an \$n \times n\$ matrix Q such that:
\$A = P D Q\$.
P and Q are unimodular ...
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Antisymmetry of a Matrix
A matrix is antisymmetric, or skew-symmetric, if its transpose equals its negative.
The transpose of a matrix can be obtained by reflecting its elements across the main diagonal. Examples of ...
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Positioning a fake mirror for best effect
Challenge
Premise
Consider a mosaic of \$m\times n\$ tiles, in \$k\$ unique colours designated by integers. Example (\$3\times6\$, four colours):
...
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Bunny Shakespeare poetry [closed]
Suppose you have a grid of cells that is 6 wide and arbitrarily tall. In each cell is a word. Let the bottom row, which is row #1, be the last 6 words of sample.txt in order. Let the second to last ...
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Borders of a Rectangular Matrix
Although it's done a few times as sub-challenge of a larger challenge, and we also have a challenge to remove the borders of a square matrix, I couldn't find a challenge to output the borders of a ...
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Print all semimagic squares [closed]
I am working on a code to print all semimagic squares [1] of a given size. I am working with the following definition:
An \$n\times n\$ consists of numbers \$1,2,\cdots, n^2\$.
All numbers must be ...
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answers
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Find the number of n-by-n (-1, 0, 1) matrices with zero permanent as quickly as possible
The permanent of an \$n\$-by-\$n\$ matrix \$A = (a_{i,j})\$ is defined as:
$$\operatorname{perm}(A)=\sum_{\sigma\in S_n}\prod_{i=1}^n a_{i,\sigma(i)}$$
For a fixed \$n\$, consider the \$n\$-by-\$n\$ ...
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votes
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Determinant of an Integer Matrix
Given a square integer matrix as input, output the determinant of the matrix.
Rules
You may assume that all elements in the matrix, the determinant of the matrix, and the total number of elements in ...
- 4,765
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votes
9
answers
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Compute the perimeter density matrix
Introduction
The perimeter density matrix is an infinite binary matrix M defined as follows.
Consider a (1-based) index (x, y), and denote by M[x, y] the rectangular sub-matrix spanned by the corner (...
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votes
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Painting with Line Filler
Given a matrix of positive integers, output whether it's possible to generate it by starting with an empty1 matrix of the same dimensions and repeatedly filling a whole row or a whole column with the ...
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0
answers
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How to divide the columns in a time series by their first value in R? [closed]
I have the code below working. But there must be a better way.
...
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14
answers
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Ragged Matrix Indexing
A ragged matrix, is a matrix that has a different number of elements in each row. Your challenge is to write a program in any favorable language to find the indices of all occurrences of target in the ...
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Construct a Gaussian Matrix
Gaussian blur is a method used for blurring images smoothly. It involves creating a matrix which will be used by convolving it with the pixels of an image. In this challenge, your task is to construct ...
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Double trace of a square matrix
Inspired by a question (now closed) at Stack Overflow.
Given a square matrix, let its double trace be defined as the sum of the entries from its main diagonal and its anti-diagonal. These are marked ...
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Remove surrounding zeroes of a 2d array
This is a 2-dimensional version of this question.
Given a non-empty 2-dimensional array/matrix containing only non-negative integers:
$$ \begin{bmatrix}
{\color{Red}0} & {\color{Red}0} & {\...
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Make a Custom Bayer Matrix
A Bayer matrix is a threshold map used for ordered dithering that gives the illusion of having more shades of color than actually present by using a crosshatch-like pattern.
Bayer matrices are square ...
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3D rotation matrix to quaternion
There are multiple ways to represent a 3D rotation. The most intuitive way is the rotation matrix –
$$A=\begin{bmatrix}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&...
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Generate a Walsh Matrix
A Walsh matrix is a special kind of square matrix with applications in quantum computing (and probably elsewhere, but I only care about quantum computing).
Properties of Walsh matrices
The ...
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Output a Latin Square
An \$n\times n\$ Latin Square is a grid containing exactly \$n\$ distinct values where the values in each row and column are distinct. For example,
$$\begin{matrix}
A & B & C \\
C & A &...
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Reconstruct Matrix from its diagonals
Given the diagonals of a matrix, reconstruct the original matrix.
The diagonals parallel to the major diagonal (the main diagonals) will be given.
Diagonals: ...
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Is this a shift matrix?
A Shift matrix is a binary matrix with one superdiagonal or subdiagonal formed by only ones, everything else is a zero.
A superdiagonal/subdiagonal is a diagonal parallel to the main diagonal, which ...
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Minimum rotation to get the maximum value
I recently solved a coding challenge in one of the challenge papers that my IT teacher gave to us. It was a seemingly simple, but fun challenge, so I thought it will make fun golfing.
The task
Given ...
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