# Tag Info

### How can I quickly judge whether matrix A is the inverse matrix of B?

You might be looking for something like Freivalds' algorithm. It is a randomized probabilistic algorithm that given three square matrices $A,B$ and $C$ checks if $A \times B = C$ by using random ...

### Real life examples of *zero* weight edges in graphs

Of course. The weight can mean things that are irrelevant to the existence of an edge. Since you don't ask for a "list of say 6 or 7 real-life examples", I will just add one. Consider a ...

### How to prove that matrix inversion is at least as hard as matrix multiplication?

If you want to multiply two matrices $A$ and $B$ then observe that \begin{pmatrix}I_n&A&\\&I_n&B\\&&I_n\end{pmatrix}^{-1}= \begin{pmatrix}I_n&-A&AB\\&I_n&-B\\&...
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### Fastest way to solve a system of linear equations

A LU decomposition of a $n \times n$ matrix can be computed in $O(M(n))$ time, where $M(n)$ is the time to multiply two $n \times n$ matrices. Therefore, you can find a solution to a system of $n$ ...

### Real life examples of *zero* weight edges in graphs

The classic strategy game Civilization by MicroProse represents the world map as a square grid where each node of the grid is a tile of the world map, representing some type of terrain. Players ...
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### Minimal basis for set of binary vectors using XOR

If you treat your vectors as over the field $GF(2)$ rather than over the set $\{0,1\}$, then what you ask is to find a basis for the span of a set of vectors. This is a well-studied problem in linear ...

### Real life examples of *zero* weight edges in graphs

In circuity, we often construct a graph of a circuit. Wires are typically modeled as 0 resistance because, frankly, measuring the resistance of wires is really tricky and rarely profitable. So if we ...

### Automated optimization of 0-1 matrix vector multiplication

This is related to an open research question, which is known as the "Online Boolean Matrix-Vector Multiplication (OMv) problem". This problem reads as follows (see ): Given a binary $n \times n$ ...

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### Automated optimization of 0-1 matrix vector multiplication

If it is possible try to exploit banded tridiagonal nature of matrix. Otherwise if the matrix contains only a constant number of distinct values (which surely is being binary), you should try Mailman ...
The classical framework is the one of bilinear algorithms and tensor rank decompositions; basically, you construct the 3-way tensor associated to the bilinear map $f(A,B) = A \cdot B$, in the basis of ...