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.
290
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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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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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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 ...
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5
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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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9
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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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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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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
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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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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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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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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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12
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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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16
answers
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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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0
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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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Find Sub-matrix with matched cell 1
You are given a matrix of size m x n where each cell can contain either 1 or 0. You need to find the largest square submatrix that contains only 1's. The output should be the area of the largest ...
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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 ...
CommunityBot
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The Hungry Mouse
Sixteen piles of cheese are put on a 4x4 square. They're labeled from \$1\$ to \$16\$. The smallest pile is \$1\$ and the biggest one is \$16\$.
The Hungry Mouse is so hungry that it always goes ...
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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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21
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11
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Is this a Jordan matrix?
Background
A Jordan matrix is a block-diagonal matrix where each block on the diagonal has the structure of
$$
\begin{bmatrix}
\lambda & 1 & 0 & \cdots & 0 \\
0 &...
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Sum of first row and column, then second row and column ... and so on
Take a non-empty matrix / numeric array containing positive integers as input. Return, in this order, the sums of the first row and column, then the second row and column and continue until there aren'...
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17
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Codegolf the Hafnian
The challenge is to write codegolf for the Hafnian of a matrix.
The Hafnian of an \$2n \times 2n\$ symmetric matrix \$A\$ is defined as:
$$\operatorname{haf}(A) = \frac 1 {n!2^n} \sum_{\sigma \in S_{...
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Vandermonde Determinant
Given a vector of \$n\$ values \$(x_1,x_2,x_3,\ldots,x_n)\$ return the determinant of the corresponding Vandermonde matrix
\$V(x_1, x_2, \ldots, x_n) = \begin{bmatrix}1 & x_1 & x_1^2 & x_1^...
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Calculate the integer square root of a matrix
Let \$A\$ be a square matrix that is at least \$2 \times 2\$ where each element is an integer. \$A^2 = A \times A\$ will then have the same dimensions as \$A\$, and will have integer elements. For ...
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Beware of the matrix tornado!
The matrix tornado is just like any other tornado: it consists of things rotating around a center. In this case, elements of the matrix instead of air.
Here is an example of a matrix tornado:
First ...
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Calculate the inverse of a matrix
Somehow, we don't yet have a challenge for finding the inverse of an arbitrarily-sized square matrix, despite having ones for 3x3 and 4x4, as well as a more complex version.
Your task is, given a ...
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Rotation summation
Take a square matrix containing positive integers as input, and calculate the "rotated sum" of the matrix.
Rotated sum:
Take the sum of the original matrix and the same matrix rotated 90, 180 and ...
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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 ...
- 17.1k
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Implement Strassen's algorithm [closed]
Strassen's algorithm was the first method of matrix multiplication in subcubic time complexity, namely O(n**log2(7)) for a pair of ...
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Make all the squares explode
You are given a square matrix of width \$\ge2\$, containing square numbers \$\ge1\$.
Your task is to make all square numbers 'explode' until all of them have disappeared. You must print or return the ...
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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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Find the representative submatrix
Note: This is a more limited version of a challenge from 2014 that only received one answer. That challenge required participants write two programs; this challenge is essentially one half of that. ...
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Find the box by its corners
Given a matrix of integers \$M\$ and a list of four integers \$L\$, find the sub-matrix \$N\$ whose corners are given by \$L\$ and return the sum of its elements.
Suppose you're given the list \$L = [...
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Make the cheapest cut
“Cut” a matrix of integers on the line where the sum of the absolute differences of “severed” neighbors is the least.
Example
Consider this matrix:
...
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Fryer simulator
Your task is to model the effects of batter on pieces of food. Please add three layers of crust.
...
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14
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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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Reconstruct a zigzagified 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 the unrolled vector along with the matrix ...
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Rotating a 2D Matrix
Let's say I have the following (2D) matrix:
[[1, 2, 3, 4 ],
[5, 6, 7, 8 ],
[9, 10, 11, 12],
[13, 14, 15, 16]]
Rotate the matrix counterclockwise ...
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Apply gravity to this matrix
This was inspired by this question.
Given an \$m\times n\$ matrix of \$0\$'s and \$1\$'s, apply "gravity" to it. This means to drop down all the \$1\$'s as if they were affected by gravity.
...
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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&...
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Box blur the string
Box blur is a simple operation for blurring images. To apply box blur, simply replace each pixel with the average of its and the surrounding 8 pixels' values. Consider, for example, the following ...
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Find a matrix whose sliding sum is the input
Given a matrix like this:
1 1 3 -2
3 -4 1 -1
1 1 1 0
0 -1 0 0
By taking a 2×2 "sliding sum", where the sum of every 2×2 region of the matrix is ...
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Reduced Row-Echelon Form of a Matrix
The goal of this challenge is to create a program that takes in a matrix and outputs its reduced row-echelon form.
A matrix is in reduced row-echelon form if it meets all of the
following ...
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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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