12/1/2022 0 Comments Permute a matrix![]() ![]() ![]() Equivalently, one may freely swap both the rows and columns of $M$.īackground: Since an algorithm has been spelt out in detail, I'll briefly explain my motivation.Įach finite (order-theoretic) lattice $L$ has an associated "poset of irreducibles" which may be viewed as the relation $R \subseteq J(L) \times M(L)$ between the join/meet-irreducibles where $R(j,m) \iff j \nleq_L m$. B permute (A,dimorder) rearranges the dimensions of an array in the order specified by the vector dimorder. However I don't have access to it, nor can I find it on his website.ĭoes anyone know of a reference, or if there has been any subsequent work?Ĭlarification: I am asking whether there exist two permutation matrices $P,Q$ such that $PMQ$ is triangular. It says here that Wilf (1997) has studied the first problem in "On Crossing Numbers, and some Unsolved Problems". permutation matrix A square matrix in which each column contains precisely one nonzero element, which is equal to unity. I am also interested in the case where "triangular" is replaced by unitriangular. Given an $m\times n$ binary matrix $M$, can we permute its rows/columns to obtain a triangular matrix? It is well known that when p is an n-cycle, A is permutation similar to a circulant matrix. Example The permute function can do the same as the transpose function. ![]()
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