# 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: ...
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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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### 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 ...
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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 $p_A(x) = \det(Ix-A)$ 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 ...
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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 ...
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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 ...
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### 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 ...
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### Find the greatest line

You will be given a 2-D array A of integers, and a length N. Your task is to find within the array the straight line (horizontal, vertical or diagonal) of N elements that yields the highest total sum, ...
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