# Questions tagged [matrix]

A matrix is a list of numbers arranged in a rectangle with rows and columns. In programming, it is also known as a 2D array. Use this tag if your challenge is about manipulating matrices.

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### Find the Cell's Neighbours

...or Toroidal Moore Neighbourhoods Given positive integers h, w and a non-negative integer ...
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### Is the matrix centrosymmetric… and so is the code?

Defintion A centrosymmetric matrix is a square matrix that is symmetric about its center. More rigorously, a matrix $A$ of size $n \times n$ is centrosymmetric if, for any \\$i,\: j \in ([1, n] \...
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### 2D Array Middle Point

Given dimensions of a 2D array, except 1xn, that results in an odd number of elements, find the midpoint index. Example: Input is 3x5, representing the 2D array [0,0] [0,1] [0,2] [0,3] [0,4] [...
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### Saddle points in a matrix

A matrix can be thought of as the altitudes of a surface in 3D space. Consider the 8 neighbours (orthogonal and diagonal) of a cell as a cyclic sequence in clockwise (or anticlockwise) order. Some ...
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### Find the Number With the Highest Sum of Neighbors

The Challenge Given a grid of numbers (10 <= N <= 99) Return number with the highest sum of the four numbers adjacent to it; that is the numbers above, below, right, and left of the number, but ...
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### Classify a region by its slope

Definitions The kth ring of a square matrix of size N, where 1 ≤ k ≤ ceiling(N/2) is the list formed by the elements of the kth and (N-k+1)th rows and columns, but without the first and last k-1 ...
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### Array-of-array string conversion to and from matrix [closed]

Matrix challenges are popular. There's an issue of how to provide test cases. A common method is the row-wise array-of-arrays representation, such as: ...
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### Is this a Weyr matrix?

There's a type of n×n matrix W called the basic Weyr canonical form. Such a matrix is described by its blocks and has the following properties, using the following reference diagram: the main ...
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### Beginners 10x10 multiplication matrix [duplicate]

I was looking for a very easy task to look how short of a code can be produced on a beginners exercise. The goal is to produce a simple table that looks like this common java/c# code is about 4 lines....
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### Sum of replicated matrices

Given a list of numbers [ a1 a2 ... an ], compute the sum of all the matrices Aᵢ where Aᵢ is defined as follows (m is the maximum of all aᵢ): ...
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### Are there mountain rings?

Challenge Given a matrix of positive integers, determine if there are any "rings" of mountains. The formal definition for this challenge is: given a matrix of positive integers, is there any positive ...
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### Progression of Matrix Columns

Consider the infinite matrix: ...
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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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### Find arsonist's lullaby

Imagine an arsonist walking around the town and picking its victims according to a very specific pattern (Or, alternatively, Imagine a bee flying around the garden and picking its flowers to pollenize ...
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### The biggest square

This question is similar to Biggest Square in a grid. Challenge Given a matrix of 1 and 0 in a string format ...
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### Getting the Vowel Square

Challenge You will create a function which takes a matrix filled with letters from the alphabet and determine if a 2x2 square composed of vowels exists. If a 2x2 ...
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### Matrix in “slash” order

Given two positive numbers N >= 2 and N <= 100 create a matrix which follows the following rules: First Number starts at ...
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### Seats in a Finnish cinema

You're given the map of a cinema theatre as a boolean matrix: 0 represents a free seat, 1 - occupied. Each Finn who walks in chooses the seat farthest away (Euclidean distance) from the nearest ...
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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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### The Lonely Islands

Input: A 2D array containing two distinct (optional) values. I'll use 0 and 1 when explaining the rules. The input format is of course flexible. Challenge: Zeros are water, and ones are islands. In ...
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### Golf A Free Lunch

Find a maximally profitable sequence of exchanges given an exchange rate table. As an example consider the currencies Ariary (your home currency), Baht, Cedi, and Denar where the rate from one to ...
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### Matrix trace for any matrix through… Bresenham’s line rasterisation

Inspired by this. Agatha Stephendale, a sophomore who is really into raster graphics, has taken a course in linear algebra. Now she imagines matrices as rectangles, but in her artistic mind, she ...
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### There, I fixed it (with rope)

Related: Rather similar (but much easier) challenge horizontally: There I fixed it (with tape) Challenge: Given a string only containing upper- and/or lowercase letters (whichever you prefer) and ...
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### Convergence of a Markov Process

Challenge Given a left- or right-stochastic matrix where the limit as x approaches infinity of the matrix to the power of x approaches a matrix with all finite values, return the matrix to which the ...
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### We ended up where we started!…

Challenge: Input: You take two inputs: - A string only containing printable ASCII (excluding spaces, tabs or new-lines) - A printable ASCII character Output: The first line will contain the string-...
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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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### Codegolf the Hafnian

The challenge is to write codegolf for the Hafnian of a matrix. The Hafnian of an 2n-by-2n symmetric matrix ...
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### How to print the below format in the fewest bytes?

This challenge is inspired by this, now deleted question. Take a positive integer N as input, and output a matrix with the numbers 1 .. N2 that follows the pattern below: Fill in the first row with ...
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### Hermitian matrix?

Note that this challenge requires no handling or understanding of complex numbers. Given a non-empty square matrix where every element is a two-element (Re,Im) integer list, determine (giving any ...
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### Minimally sort a list into a matrix

Given an unsorted list of unique strictly positive integers, minimally sort it into a 2D matrix. The input list is guaranteed to be of composite length, which means the output matrix is not ...
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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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### Flattened Spiral Permutation Index

Context Consider square matrices with n columns and rows containing the first n^2 (i.e. n ...
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### Friar simulator

The brethren from the order of St Golfus the Concise have a tradition of reciting a short prayer whenever they see someone make the sign of the cross. Due to the high level of sin measured among ...
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### Perfect Squares Without Borders

Given n=m^2, return a list of integers that do not border the m x m grid of integers from ...
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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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### Matrices Generated Using Rectangles

Input is an r by c matrix of non-negative integers (you may input r and c as other parameters if this helps with golf). This may be inputted as a 2D array or, if you prefer, a 1D array (though taking ...
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### Generalized matrix trace

Inspiration. Given (by any means): A two-argument (or single argument consisting of a two-element list) black box function, f: ℤ+ × ℤ+ → ℤ+ (input and output are ...
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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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### Compute the Optimal Square Matrix

The optimal matrix (for the rather narrow scope of this challenge) is obtained by "zipping" the elements from the corresponding rows and columns of a square matrix and getting the maximum of each pair....
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### Queue Our Decomposition

In this challenge I will ask you to find a QR decomposition of a square matrix. The QR decomposition of matrix A is two Matrices Q and R such that A = QR. In particular we are looking for Q to be an ...
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### lexicographically sorted list of index [closed]

Given a drawing of the letter shoot system, where an existing piece of pipe is marked with a *, and an empty spot is marked with a ., your task is to compile a lexicographically sorted list of index ...
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Definition An arrowhead matrix is a matrix that has all entries equal to 0, except the ones on the main diagonal, top row and leftmost column. In other words, the matrix should look like this: * * * ...
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### Characteristic polynomial

The characteristic polynomial of a square matrix A is defined as the polynomial pA(x) = det(Ix-A) where I is the identity matrix and det the determinant. Note that this definition always gives us a ...
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### Advent Challenge 7: Balance the storage carts!

<< Prev Next >> After some careful analysis, Santa was able to determine the dock size ranges and get the presents into the correct transportation dock. Now, he needs you to help him balance ...
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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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### Eigenvalues of a Matrix

Given a square matrix, output the matrix's eigenvalues. Each eigenvalue should be repeated a number of times equal to its algebraic multiplicity. The eigenvalues of a matrix ...
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### Is my kids' alphabet mat properly grouped by colors?

My kids have an alphabet mat to play with, something like this: After months with the tiles of the mat randomly placed, I got tired and placed all the tiles of the mat grouped by sections according ...