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Questions tagged [matrices]

For questions about construction and modification of matrices, objects represented by 2-dimensional arrays that are used to define linear operators within linear algebra.

48 questions with no upvoted or accepted answers
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8
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156 views

Can you multiply complex 2x2 matrices in fewer than 21 real multiplies?

It is well known that 2x2 matrices can be multiplied using just 7 (instead of the obvious 8) multiplications in the ground field (Strassen-Winograd, etc.). It is also well known that complex numbers ...
5
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0answers
142 views

A matrix rank problem over finite fields

I have already asked a similar question here, but since I have not got an acceptable answer, I decided to ask a simpler version of the question here. Let $M|\mathbf w$, where $M$ is a matrix and $\...
4
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0answers
67 views

Is this a known question in matrix sketching?

Say one has a $D \times n$ matrix $A$ all of whose entries are non-zero. One wants a method which will look at each of the columns of $A$ one by one and create new $m \ll D $ dimensional columns and ...
3
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0answers
52 views

Heuristic for making set of indexes in an array/matrix with generating functions/patterns

I am trying to find a lead on how to solve or find a heuristic the following kind of problem: Given an array/matrix with entries of only 1s and 0s, using a set of looping functions/patterns of a ...
3
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0answers
88 views

How to determine Isomorphism of Non-Symmetric Matrix when Permutation-Set is given?

Consider, two $m \times n$ matrices $A, B$ such that there is a permutation $\kappa$ that such that such that $A^{\kappa}=B$ (Wielandt's notation), i.e. $A, B$ are isomorphic but not equal. Since,...
3
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0answers
409 views

computing permanent of a 0-1 rectangular matrix

I need to compute the permanent of a 10*100 matrix. All the entries are either 0 or 1. All I know is that I can compute the permanent of all 10*10 submatrices and then sum it to get the desired ...
2
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0answers
39 views

Check if a matrix over finite fields is superregular

Is there any practical, efficient algorithm to check if a matrix over $\mathbf{F}_{p^n}$ is superregular? It need not be theoretically polynomial, just roughly be implementable for $n=32$ and for ...
2
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0answers
45 views

How many iterations of Lanczos bidiagonalization are required in order to obtain the first k singular values/vectors of a matrix?

I am trying to implement a fast SVD algorithm for obtaining the first $k$ singular values/vectors of an $M\times N$ matrix ($k < \min(M,N)$) using the following 2-step process: 1) bidiagonalize ...
2
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0answers
40 views

mx2m modulo-3 matrix solution

Is there an efficient algorithm for the following problem? Given: a $m$-vector $b \in \{0,1,2\}^m$, and a $m \times 2m$ matrix $A$, with the promise that for every $b' \in \{0,1,2\}^m$, there exists $...
2
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0answers
237 views

What is the Time Complexity of the Matrix Exponential?

While trying to compute the Matrix Exponential of an nxn array I decided to take advantage of a Python function called ...
2
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0answers
332 views

Computational complexity of Doolittle's algorithm

I could not find a big-oh cost for Doolittle's algorithm for LU decomposition of a matrix online, so I took a pseudocode implementation from here and analyzed it to get $$\frac13n^3+\frac32n^2+\...
2
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0answers
330 views

What can I do with this algorithm?

Problem Statement The problem is to calculate the coefficients $A_{j_1\cdots j_n}$, of a square matrix A with size $N$ by $N$ of complex double elements, whose weighted sum with $N^2$ irreducible ...
2
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1answer
69 views

Find the nearest sum to a given number of two elements in sorted matrix

Given a sorted $n\times n$ matrix $A$ of real values. That is $a_{ki}<a_{kj}$ and $a_{it}<a_{jt}$, when $i<j$. Propose and algorithm, finding two elements of this matrix with the sum nearest ...
2
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1answer
116 views

How does RAID-5 algorithm locate the right device?

Please consider the following diagram of a RAID-5 array (Ignore the gray background): Now, given a logical address, how can one return the device number (0-3)? For example, DeviceByLogicalSector(50) ...
2
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1answer
445 views

Implementing the Schur decomposition of a matrix

I'm trying do implement the Schur decomposition of a matrix, but I can't find any good articles for the theory. Could someone share one?
1
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0answers
12 views

Does integer matrix multiplication with its transpose (A^T)*A have more efficient parallel algorithm than the use of symmetricity?

Integer matrix multiplication with its transpose (A^T)A gives symmetric matrix, so, only one half of it should be computed. Besides, the formula for the resulting element rik=Sum[aijajk, j] reduces to ...
1
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0answers
20 views

Minimal subset of rows that generate smaller polyhedron

Given a matrix $[A|B]$ I want to find a minimal matrix $[A'|B'] \subseteq [A|B]$ (i.e. the rows in $[A'|B']$ are also in $[A|B]$) such that $A'x < B' \Rightarrow Ax < B$. Geometrically, I want ...
1
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0answers
31 views

Minimize number of math operation of a specific matrix vector multiplication?

Let's say we have a Matrix M and a column vector v like below multiply equals Assume we can only perform multiplication, addition and substraction operation. With normal approach we need 3 ...
1
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0answers
45 views

The maximum number of uniquely intersected elements from the all possible intersection scenarios among the sets in a two-column matrix

Let us define a $n \times 2$ matrix M consisting of integer sets, such that the first column consists of the so-called intersecting sets, and the second column ...
1
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0answers
54 views

Matrix with zero spectral radius

I need an algorithm which generates a random matrix with spectral radius equal zero. The only solution I have so far is to generate two vectors $v,w$, normal onto each other ($v\perp w$), and then ...
1
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0answers
33 views

Counting on a matrix

I have an $n \times m$ matrix, and fill it with numbers of $1 \dots k$. If a matrix can be turned into another matrix by exchanging its lines and exchanging its columns, the two matrices are ...
1
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1answer
72 views

Could a Van Emde Boas tree be used for storing matrices?

I'm aware that typical techniques to store matrices in sparse form are compressed formats or maps where the key is the pair of indices and value the value of the entry in a matrix. I was wondering if ...
1
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0answers
63 views

Sparse Matrix inversion without actual inversion

I want to know what are the efficient way to invert a Sparse Matrix? Are there any algorithm,linear algebra or expansions that make this task easier with out actually inverting the matrix? Thank you ...
1
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0answers
85 views

Which algorithms provide high compression ratios for bit matrices?

I have an x*y bit matrix where the total number of bits fluctuates between ~1,000,000 and ~20,000,000 bits. The rows are much smaller than the columns. An example matrix might be of size 1,000,000 x ...
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0answers
26 views

Hebbian rule doesn't get to a fixpoint

I'm trying to implement an Hopfield Network for pictures of 32x32 bits either 1 or -1; I have these 3 pictures and I transform each of them in a vector of 1024 elements. Then I take the 3 vectors and ...
1
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0answers
199 views

How to solve linear system with modulus operation?

I came across linear equation $G(x,y) = g_k(x,y) l_k(x,y)$ mod $(y^{2^{k}})$ while reading factoring algorithm see section 3 for bivariate polynomials. I need to find the $G(x,y)$ and $l_k(x,y)$. ...
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0answers
102 views

Generate a graph to exact size using Kronecker product graph model

In network science, we can take sample a complex system and derive from this sampling a representative network (or graph) that describes the system to some extent. A model of a network, is a powerful ...
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0answers
38 views

Clustering of matrices

I have a matrix of n lines and T columns, containing only 0's or 1's. I would like to make permutations of lines (and lines only) to make the largest submatrix of 1's possible (i.e. i want to find ...
1
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0answers
52 views

How to find (real-valued) roots of matrix polynomial

Assume you have a fixed ($d=O(1)$ for that matter) degree matrix polynomial $$P(X)=A_0+A_1\cdot X+A_2\cdot X^2+\ldots+A_dX^d$$ Where $A_0,A_1,\ldots A_d\in\mathbb N^{n\times n}$ are given as input. ...
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0answers
27 views

Approximation scheme for finding best product of matrices that minimizes $||Ax - y||$ for given $x,y$

Given a set of $N$ $n \times n$ matrices $A_1,\ldots,A_N$, and two vectors $x,y$, the problem is to find a product of up to $K$ matrices $A = A_{j_1}A_{j_2}\cdots A_{j_k}$ so that $Ax$ is as close to $...
1
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0answers
113 views

Laplace's Approximation for graphical models

A question about Laplace's approximation: In Laplace's method, we need to find the mode of a function and take second order Taylor's expansion. The first order term will vanish (since the gradient is ...
0
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3answers
40 views

How much can matrix multiplication algorithm be parallelized?

You all may know that simple Matrix Multiplication algorithm: ...
0
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0answers
56 views

How to solve this dynamic programming puzzle on matrix?

We are given 4 integers N,M ,Q and Z. Initially,the matrix has all zeroes in it. We have to perform Q operations on the matrix. In each operation, any cell of the matrix can be selected(same cell ...
0
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0answers
25 views

Minimum amount of rectangles to create a 2-dimensional matrix

From this codegolf question. Consider an $r$ by $c$ matrix of nonnegative integers, called $M$. You also have a zero matrix of the same dimensions, called $N$. A "move" consists of replacing a ...
0
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0answers
26 views

Finding fixed size submatrix with highest sum

I have a matrix, which has N rows and M columns. I need to find n rows and m columns, which has the highest sum. Matrix consists of positive numbers. Not optimal solutions are ok. For example N=M=4; n=...
0
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0answers
43 views

Minimum number queries on matrix

As part of a solution to an earlier question, I am interested in the following problem. I have a 2-D matrix $M$. I want to preprocess it in linear time so that I can answer queries of the following ...
0
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0answers
61 views

Finding disjoint paths between any number of cell pair marked in nXn matrix

What should be algorithm to find all the disjoint paths between any number of pairs of cells given in matrix? We will say two paths will not intersect if there there is no cell common between any two ...
0
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0answers
9 views

Clarification on descending direction in optimization of function

Could someone clarify for me why given $f:\mathbb{R}^n \rightarrow\mathbb{R}$ to optimize an iterative function according to : $p^k=-M\nabla f(x^k)$ for $p^k$ to be descending direction the matrix M ...
0
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0answers
27 views

Equivalent Algorithm with Sharman Morrison inversion

I am trying to invert a matrix using Woodbury identity. The inversion using Cholesky decomposition has the following pseudo-code: For $t=1,2,...$ $(1)\;\; \text{Read}\;x_t\in\mathbb{R}^n$ ...
0
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0answers
2k views

Algorithm (Addition of two matrices)

A file F holds the non-zero elements of two large n×n matrices, A and B. The matrix entries are stored as triplets (i,j,value), where value is the (i,j)th element of a matrix. The file first stores ...
0
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0answers
86 views

What is the run time of this algorithm?

Robot in a grid: Imagine a robot sitting on the upper left corner of a grid with $r$ rows and $c$ columns. The robot can only move in two directions, right or down, but certain cells are off limits ...
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0answers
39 views

How do Perwitt and Sobel detect edges?

I read up on the Perwitt operator and it detects two types of edges (vertical and horizontal). The Sobel operator on the other hand does the same as the Perwitt except that the masks are not constant ...
0
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0answers
180 views

3D Column Sort (Leighton) Algorithm

Suppose you have a matrix A (9x3) of Real numbers and want to sort in columnwise. In this case we can use Leighton ColumnSort algorithms to achieve this. But question is, how can I sort 3 dimensional ...
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0answers
143 views

Find all sets of n unique rows in matrix

I am looking for an efficient method to find all unique combinations of $n$ rows in a matrix. For example, if $n=6$, then I want to find all sets of 6 rows from the input set C in which the columns ...
0
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0answers
380 views

Calculate the computational complexity of multiplication AxAT

I need to implement an algorithm that calculates the symmetric matrix obtained by performing $A A^t$ being $A^t$ the transpose of $A$. I did my analysis from two perspectives: The first thing I ...
0
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0answers
69 views

Immutable data structures for 2d+ lattices

I would like to find an immutable/persistent data structure that allows efficient updating for 2d (or higher) lattices/arrays/matrices, and reasonable performance when appending in any direction. ...
0
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0answers
326 views

Generate a Random Diagonally Dominant Matrix

I would like to write a function to generate a diagonally dominant matrix of random values. What I'm ultimately leading to is writing a code to implement the Jacobi method on this matrix in CUDA for a ...
-1
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1answer
106 views

Maximum frequency in any row and column

I have been given 2D matrix with some elements. I want to find out what is maximum frequency in any row and column. Example: 1 2 1 2 3 4 1 2 1 1 1 1 2 2 2 2 Maximum frequency is 6 which occurs in last ...