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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18
votes
5answers
594 views

Is it an elementary matrix?

Consider a linear system of equations, in \$n\$ unknowns, expressed as $$A \textbf x = \textbf b$$ where \$A \in M_{n,n}(\mathbb Z)\$ is an \$n \times n\$ matrix of integers, \$\textbf x\$ is a column ...
19
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13answers
1k views

Compute matrix blockiness

Consider a non-empty binary matrix M and a natural number n. For the purposes of this challenge, M is said to have blockiness n if it can be built using adjacent square blocks of size n, where each ...
16
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10answers
755 views

Remove submatrices

Given two integer matrices a and b, your challenge is to replace any occurences of b in <...
6
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1answer
455 views

Fast Matrix Multiplicator Evaluator

A triplet of real tensors \$(A,B,C)\$ of size \$\gamma \times \gamma \times \sigma\$ represents a matrix multiplication algorithm with \$\sigma\$ elementary multiplications iff the following function ...
20
votes
9answers
2k views

Bird's Algorithm for Computing Determinants

There is a division-free algorithm for computing determinants published by R.S.Bird in 2011 that uses only matrix multiplications. Given a \$n×n\$ matrix \$X\$, the matrix \$Y=μ(X)\$ is another \$n×n\$...
20
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19answers
2k views

Checkered grid with X mark

Challenge Given two integer values \$a \ge 2\$ and \$0 \le b < a\$, generate a \$(2a-1) \times (2a-1)\$ matrix consisting of the integers 0, 1, and 2 as follows: Create a checkerboard of 0s and 1s ...
22
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17answers
2k views

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 ...
11
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8answers
1k views

Find the number of paths in a n×n grid

Information Given a non-negative odd integer (let's call it \$n\$), find the number of all possible paths which covers all squares and get from the start to end on a grid. The grid is of size \$n\$×\$...
16
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15answers
1k views

Drop down the numbers

This was inspired by Apply gravity to this matrix Your challenge is to input a matrix with non-negative one-digit integers and drop down the 1's down 1 column, the 2's down 2 columns, the 3's down 3 ...
21
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24answers
3k views

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. ...
18
votes
4answers
554 views

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 ...
19
votes
7answers
2k views

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 &...
29
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26answers
2k views

Recursive Z-matrix

Originally from a CMC I proposed for the last BMG event Challenge Given a non-negative integer \$n\$, create a 2D array of size \$2^n × 2^n\$ which is generated in the following manner: Divide the ...
15
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9answers
529 views

To raise \$ e \$ to the power of a matrix

Inspired by this 3Blue1Brown video Given a square matrix \$ M \$, compute its matrix exponential \$ \exp(M) \$, which is defined, using an extension of the Maclaurin series for \$ e^x \$, as $$ \exp(M)...
18
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11answers
2k views

Count my Pluses

Your task is, to count how many pluses I have. What Pluses? The no plus: 0 Points - The naïve Plus: 1 Point + The double ...
16
votes
7answers
1k views

Drop some boxes

Say I have a pile of boxes: AAA BBB I can create it in two steps: BBB ↓ (empty) --- AAA ↓ BBB But with this: ...
14
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17answers
769 views

Square chunk my matrix

Your challenge is to write a function/program that takes a matrix of integers m and a number n as input and: Splits m into n by n chunks Replaces each chunk with the most common value in that chunk (...
25
votes
9answers
2k views

Is it a valid Parker Square

5 Years ago, this happened, and then it became sort of a meme. Challenge The Challenge today is, to check if a "magic square" is a valid parker square. What is a Real Magic square? All the ...
23
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39answers
2k views

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\$, ...
9
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15answers
745 views

Construct a Modulo Multiplication Table

Consider a n x n multiplication table and replace each item with its remainder of division by n. For example, here is a ...
26
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21answers
3k views

I'm Lazy*: Top-left align my text

* and don't have a word processor with top-left align support :D Take several lines of input, with at least four unique characters of your choice including newline and space. The input can also be ...
22
votes
2answers
947 views

Minecraft piston pushing

In Minecraft, pistons are blocks that can move other blocks. However, they can only move at most twelve blocks, and won't work at all if any obsidian is in the way. Also, slime blocks are sticky and ...
22
votes
44answers
2k views

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 &...
12
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4answers
482 views

The Game of Cat And Mice | With Matrices

Challenge This coding challenge is to figure out how many rounds the cat can live. In a \$4\times4\$ matrix, there are a number of mice and exactly 1 cat. Example: $$ \begin{array} {|r|r|}\hline 🐭 &...
16
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5answers
727 views

Dominate a zero-sum game

Consider a zero-sum game with 2 contestants. Each round, each contestant chooses, independently of each other, one of \$n \ge 2\$ different choices. Depending on the two chosen choices, one player is ...
45
votes
21answers
2k views

Summon the sevens

You are given a \$3\times3\$ square matrix where each cell is any digit between \$0\$ and \$9\$ except \$7\$. Your task is to figure out the minimum number of digits that must be replaced with \$7\$'s ...
8
votes
3answers
662 views

Validating a Battleship board

Do you know the game Battleship? Well, I want to play with my little brother, but before we can begin we need to set up our ships on the board. This is your input. Now, we need to check that the ships ...
28
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10answers
2k views

Help Stack Exchange transpose tables

Stack Exchange doesn't know how to transpose tables. Let's help. Given a markdown table, transpose it. Input assumptions: There will be at least two rows (including header) and two columns Either all ...
29
votes
20answers
3k views

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 ...
10
votes
1answer
232 views

Thin Paper Folding

Thin Paper Folding This is a "lighter" version of the challenge Paper Folding for the win. This challenge is being posted as a different challenge with many modifications in order to try ...
26
votes
24answers
2k views

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 ...
18
votes
1answer
352 views

Paper Folding for the win

Paper Folding for the win "How many times can you fold a paper?" - This well known question led to many arguments, competition, myths and theories. Well, the answer to that question depends ...
15
votes
13answers
1k views

Help me accelerate linear recurrence relation!

Background A linear recurrence relation is a description of a sequence, defined as one or more initial terms and a linear formula on last \$k\$ terms to calculate the next term. (For the sake of ...
20
votes
1answer
483 views

Checkerboard the Matrix

Task Given a matrix, your program/function should output a row-equivalent matrix in checkerboard form ( \$A_{ij}=0\$ if and only if \$i+j\$ is odd). Two matrices are defined to be row-equivalent if ...
19
votes
10answers
2k views

Complete the Magic Square

Background A magic square is an n×n matrix consisting of one of each of the integers from \$1\$ to \$n^2\$ where every row, column, and diagonal sum to the same ...
9
votes
0answers
189 views

Cover positions with snakes of same 'colour'

Imagine a grid where the origin square \$(0,0)\$ is at the top left of the screen, and positive \$x\$ is rightwards whereas positive \$y\$ is downwards. Coloured squares are at various positions on ...
14
votes
5answers
966 views

What is the Subspace Dimension?

Challenge Given the Cartesian coordinates of two or more distinct points in Euclidean n-space (\$\mathbb{R}^n\$), output the minimum dimension of a flat (affine) subspace that contains those points, ...
26
votes
21answers
2k views

Logo Pack LAPACK

This is the logo for LAPACK, a widely used software library for numerical linear algebra. Your task is to print the logo (color and matrix brackets not required) as this exact string. Trailing ...
15
votes
3answers
280 views

Identify the smallest possible tile in the matrix

Challenge Given a matrix of digits (0-9), find the smallest (in terms of area) rectangular matrix of digits where one or more copies of itself, possibly rotated, can tile the original matrix. ...
2
votes
2answers
188 views

Create a text image by manual automation

Challenge Premise It's 2006, and Alice is trying to send Bob their her completed notes on their newly ended expeditions into the labyrinthine school library, which the two of them found suffers from a ...
21
votes
6answers
2k views

The matrix has U

Given a matrix of size at least 3×3 formed by positive integers, determine if it contains at least one "U" pattern, defined as ...
12
votes
7answers
704 views

Toroidally magnify-blur a matrix

Task Given a matrix of numbers \$M\$ with \$r\$ rows and \$c\$ columns, and the magnification factor \$n\$, build the matrix with \$rn\$ rows and \$cn\$ columns where the original elements are spaced ...
11
votes
1answer
317 views

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): ...
17
votes
3answers
693 views

Make a rectangle from a collection of (sliced) squares

Inspired by Make a Rectangle from a Triangle. Task There is a famous formula on the sum of first \$n\$ squares: $$ 1^2 + 2^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6} $$ It is known that this number ...
22
votes
17answers
3k views

Make a Rectangle from a Triangle

You can depict a triangular number, T(N), by writing one 1 on a line, then two 2's on the line below, then three 3's on the line below that, and so on until N N's. You end up with a triangle of T(N) ...
19
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16answers
1k views

(RGS 4/5) Inverting matrices modulo m

Task Given an integer matrix M and a modulus m, find an inverse of M modulo ...
17
votes
10answers
521 views

Decomposition of a matrix in \$ SL_2(\mathbb{Z}) \$

Background The special linear group \$ SL_2(\mathbb{Z}) \$ is a multiplicative group of \$ 2 \times 2 \$ matrices whose elements are integers and determinant is 1. It is known that every member of \$...
22
votes
2answers
759 views

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\$ ...
19
votes
21answers
2k views

Clockwise matrix rotation

The title pretty much describes it all. Given as input a \$n \times m\$ matrix and an integer \$i\$ create a complete function/program that returns the matrix \$i\$ times clockwise rotated by \$90^\...
11
votes
17answers
10k views

Euclidean Distance Between Two Matrices

Your task is to write the shortest algorithm in a language of your choosing that accomplishes the following: Given two matrices it must return the euclidean distance matrix. The euclidean distance ...

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