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Path: utzoo!watmath!ljdickey
From: ljdickey@watmath.UUCP
Newsgroups: net.math,net.lang.apl
Subject: Matrix Inverses
Message-ID: <5657@watmath.UUCP>
Date: Thu, 25-Aug-83 10:57:21 EDT
Article-I.D.: watmath.5657
Posted: Thu Aug 25 10:57:21 1983
Date-Received: Fri, 26-Aug-83 08:46:30 EDT
Sender: ljdickey@watmath.UUCP
Organization: U of Waterloo, Ontario
Lines: 28

This is a reposting of an article that got trashed somewhere along
the net, before it got to Whippany.  If this is a repeat for you, sorry.

The other day I was trying out a new version of APL for the IBM PC.
One of the things that I tried was finding the inverse of a matrix.
The expression that I used found the inverse of a 10 by 10 matrix 
with integers chosen randomly from 1 to 1000.  I had executed

          domino   ?  (10 10)  rho  1000

and the PC did the calculation in about 8 seconds.

After I had done this, I wondered about the matrix that had been
chosen.  What were the chances that it would be singular?  I have
tried a few more, and all had inverses.  So here is the question:

         Given a matrix that is   N by N   whose entries
         are chosen (with replacement) from the set
         {1, 2, 3, ... , K}, what is the probability
         (as a function of N and K) that the 
         determinant of the matrix is zero?


-- 
	Lee Dickey		(ljdickey@watmath.UUCP)
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				University of Waterloo