# 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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### 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: ...
434 views

### 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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Given a list of numbers $[a_1, a_2, ... a_n]$, compute the sum of all the matrices $A_i$ where $A_i$ is defined as follows ($m$ is the maximum of all $a_i$): $$\begin{array}{c|cc} &... 15 votes 3 answers 347 views ### 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 ... 17 votes 16 answers 780 views ### Progression of Matrix Columns Consider the infinite matrix: ... 27 votes 58 answers 3k views ### 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 ... 26 votes 12 answers 2k views ### 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 ... 9 votes 15 answers 923 views ### 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 ... -2 votes 11 answers 2k views ### 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 ... 23 votes 23 answers 3k views ### 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 ... 53 votes 12 answers 7k views ### 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 ... 27 votes 21 answers 4k views ### 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 ... 10 votes 2 answers 422 views ### 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 ... 27 votes 3 answers 1k views ### 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 ... 14 votes 5 answers 388 views ### 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 ... 10 votes 7 answers 2k views ### 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 new-... 11 votes 9 answers 1k views ### 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 ... 29 votes 7 answers 2k views ### 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-... 32 votes 34 answers 3k views ### 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 ... 25 votes 17 answers 3k views ### 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_{... 3k views

### 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 1,...
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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 ... 669 views

### 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 $p_A(x) = \det(Ix-A)$ where $I$ is the identity matrix and $\det$ the determinant. Note that this definition ...
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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 ... 690 views

### 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 ...
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### 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: ...
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### Minimum rectangle cover

Rectangle covers Suppose you have a matrix of bits, for example the following. 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 ...
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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 ... 509 views

### Expand an Array

Expand an array to all directions by duplicating the outer elements You will be given two inputs: an array and the expansion degree For example if I give you ... 