Talk:Unimodular matrix

message: Examples of totally unimodular matrices?
Charles Matthews 10:14, 13 Apr 2004 (UTC)
thread_title: [Untitled]

message: I strongly think that you need an additional restriction of unimodular matrices being integer matrices.
Some sources ("Loop Parallelization", Utpal Banerjee) require the inverted matrix to be an integer matrix, even though I think this is unecessary.
--M1ck1 12:10, 1 December 2006 (UTC)
thread_title:  integer matrices 

message: I find a variety of definitions for “Unimodular” on the web as of 2007 Mar 15.
This Wikipedia article presumes a matrix over Z, the integers with determinate = ±1.
<a href=http://planetmath.org/encyclopedia/UnimodularMatrix.html>Planet Math</a> requires a square matrix over some field and determinant = 1.
<a href=http://mathworld.wolfram.com/UnimodularMatrix.html>Wolfram</a> requires real elements with det = 1 but generalizes by allowing elements from some polynomial domain if the matrix has an inverse in the same domain.
(This suggests ring elements, requiring inverse matrix over same ring.)
<a href=http://www.amazon.com/Analysis-Manifolds-Physics-Part-I/dp/0444860177>Analysis, Manifolds and Physics</a> (page 173 in my edition) specifies real entries and det=1.
All of these are groups but are generalizations in different directions.
In physics contexts it seems to be a real matrix with det=1.
Perhaps there needs to be a category split between the discrete and continuous cases.
I have no idea what they should be called.
Wikipedia has a good disambiguation pattern for cases where one word applies to different subjects. —The preceding unsigned comment was added by NormHardy (talk • contribs) 05:19, 16 March 2007 (UTC)
thread_title:  Other concepts of "unimodular matrices" 

message: o.O shouldnt that be M? —The preceding unsigned comment was added by 141.3.160.82 (talk) 11:03, 10 May 2007 (UTC)
thread_title:  Mx=b where b is an integer matrix 

message: Naive question: A unitary matrix U has the property |det(U)|=1. Why is there no mention of unitary matrices in the unimodular matrix article and vice versa?  I'm curious to know how they're related and under what circumstances matrices can be both unitary and unimodular.
--Error9312 (talk) 20:25, 3 March 2009 (UTC)
thread_title:  Unitary Matrices 

message: I learned that a unimodular matrix may have determinant -1 or 1 or 0. Unfortunately I do not have another source of this than my university script. -- Phil1881 (talk) 14:29, 23 August 2010 (UTC)
thread_title:  determinant = zero 

message: Under the definition given,
A totally unimodular matrix (TU matrix) is a matrix for which every square non-singular submatrix is unimodular. 
I would believe that a matrix which has only singular square sub-matrices is also totally unimodular.  Is this correct?
Or should the definition read
A totally unimodular matrix is a matrix for which every square submatrix is non-singular and unimodular?
Ngvrnd (talk) 15:44, 9 May 2011 (UTC)
replies: text: Indeed such a matrix is totally unimodular. But if you request that every submatrix is singular, then also the 1x1 matrices are, that is, the matrix is a zero matrix. But it is totally unimodular. Your 2nd definition does not make sense, as the 1x1 matrices must all be non-singular and hence not 0. MatthiasWalter (talk) 16:11, 11 November 2011 (UTC)
thread_title:  degenerate case? matrix, having only singular square submatrices is totally unimodular? 

message: Is it common / okay to add the following link as it is the (to the best of my knowledge) only implementation of a decomposition-based implementation for testing TU. It is also quite fast and outperforms all the trivial algorithms.
* Software for testing total unimodularity by M. Walter and K. Truemper
MatthiasWalter (talk) 16:18, 11 November 2011 (UTC)
thread_title:  link to software for testing TU?

message: Article correctly asserts that a unimodular matrix must be square. Further down the page, at the network flow example, it shows a non-square matrix as an example of a unimodular matrix. Please fix. 101.170.213.70 (talk) 23:37, 25 September 2012 (UTC)
thread_title:  Square or non-square? 

message: What is the meaning of the last paragraph? I understand: "If the ring is a field, then the matrix is invertible over the ring iff it is invertible over the field", which seems to be trivial.  — Preceding unsigned comment added by Maformatiker (talk • contribs) 11:30, 26 July 2016 (UTC)
thread_title:  Abstract linear algebra 

message: That should be SL_n(Z). 
Volker1308 (talk) 17:10, 20 December 2019 (UTC)
replies: text: I don't pretend to be a number theorist, yet I think that GL_n(Z) is correct. Note that the determinant of a unimodular matrix can be -1, which doesn't appear to be the case for SL_n(Z). Sanpitch (talk) 05:26, 16 April 2020 (UTC)
thread_title:  The unimodular matrices of order n form a group, which is denoted GL_n(Z).