# Questions tagged [matrix-product]

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### Dynamic matrix-matrix multiplication

Suppose A and B are initial Boolean matrices. Let C = A*B. Suppose one can perform the sequence of the next operations: "set A[i,j] = 1", "set B[i,j] = 1". The result of each ...
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### Evidence that matrix multiplication is not in $O(n^2\log^kn)$ time

It is commonly believed that for all $\epsilon > 0$, it is possible to multiply two $n \times n$ matrices in $O(n^{2 + \epsilon})$ time. Some discussion is here. I have asked some people who are ...
105 views

### Fast Finding Main Diagonal of Matrix Multiplication

Suppose we have two matrices $A_{m\times n}$ and $B_{m\times m}$. Such that $B$ is a symmetric positive definite matrix. Is it possible to compute main diganoal of $A^TBA$ in $O(n\times m)$?
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### Trying to find Warren D. Smith's Matrix Multiplication article

One of my favorite articles on the complexity of matrix multiplication has gone dark. Warren Smith, Fast Matrix Algorithms And Multiplication Formulae, https://math.cst.temple.edu/~wds/matgrant.ps ...
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### “Matrix complexity” - is it possible?

While browsing old CStheory.se posts, I ran across a fascinating blog post on the matrix mortality problem. Unless I've misinterpreted the problem, it states that given a finite collection of 3 x 3 ...
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### state-of-the-art bit complexity of the determinant

I'm trying to understand the full bit-complexity of computing the determinant of an $n\times n$ integer matrix, with each entry represented by $M$ bits. I would like to know what is the state-of-the-...
272 views

### Commutative matrix multiplication algorithms

What is known about commutative algorithms like Winograd algorithm and its variants for Matrix Multiplication? Why is there not much study on them? Can they be asymptotically as efficient as Non-...
272 views

### the product of a matrix and a permutation matrix [closed]

Can a permutation matrix (P) be used to change the rank of another matrix (M)? Is there any literature to this effect, or to the contrary? I've tried a few small examples and the resulting matrix (M2)...
589 views

### Matrix multiplication algorithms for research

I am implementing a matrix library for use in my research. This should support 2D matrices of size 100x100 (or more perhaps later on). I am a little confused about the algorithm I should be using for ...
196 views

### the largest element of a matrix product

Given two matrices, I'm interested in finding the largest element of their product. I wonder if it's possible to do it significantly faster than the matrix multiplication the solution seems to require?...
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### Determinants and Matrix Multiplication - Similarity and differences in algorithmic complexity and arithmetic circuit size

I am trying to understand the relation between algorithmic complexity and circuit complexity of Determinants and Matrix Multiplication. It is known that the determinant of an $n\times n$ matrix can ...
517 views

### Bigger picture behind the choice of matrices in the Strassen algorithm

In the Strassen algorithm, to compute the product of two matrices $\mathbf{A}$ and $\mathbf{B}$, the matrices $\mathbf{A}$ and $\mathbf{B}$ are divided into $2 \times 2$ block matrices and the ...
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### All Pairs Shortest Path - Directed graph with integer weights

I don't understand how Distance Product works (or Min Plus Product). If we replace each argument in $A$ from $a_{i,j}$ to $x^{a_{i,j}}$ and each argument in $B$ from $b_{i,j}$ to $x^{b_{i,j}}$ and ...
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### What about apply maxplus algebra for all-pairs shortest paths?

I didn't find deep informations on Wikipedia about all-pairs shortest path, in particular I do not know what is the best algorithm to solve this problem beyond Floyd-Warshall's one, then I do not know ...
425 views

### Capacity of Uniquely Solvable Puzzle (USP)

In their seminal paper Group-theoretic algorithms for matrix multiplications, Cohn, Kleinberg, Szegedy and Umans introduce the concept of uniquely solvable puzzle (defined below) and USP capacity. ...
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### The computational complexity of matrix multiplication

I am looking for information about the computational complexity of matrix multiplication of rectangular matrices. Wikipedia states that the complexity of multiplying $A \in \mathbb{R}^{m \times n}$ by ...
407 views

### How can a problem have complexity $O(n^{2+\epsilon})$ for all $\epsilon > 0$?

For instance, it is believed that for any $\epsilon>0$ there is an algorithm for matrix multiplication that runs in $O(n^{2+\epsilon})$, but possibly no algorithm that runs in $O(n^2)$. How is this ...
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### Multiplication of circulant matrices with a diagonal matrix

Let $A_{i}$, $B_{i}$ be a sequence of circulant matrices of size $n \times n$. We know that $\sum_{i=1}^{n}A_{i}B_{i}$ can be calculated in quadratic time (use FFT to diagonalize and add the diagonal ...
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### Quantum matrix multiplication?

It doesn't seem like this is known - but are there any interesting lower bounds on the complexity of matrix multiplication in the quantum computing model? Do we have any intuition that we can beat ...