ljdickey@watmath.UUCP (08/21/83)
e always found an invertible matrix. No singular matrices so far. So, I have this question: Given an N by N matrix with integer entries chosen (with replacement) from the set of integers {1, 2, 3, ..., K}, what is the probability, as a function of N and K, that the determinant of the matrix will be zero? -- Lee Dickey (ljdickey@watmath) University of Waterloo
ljdickey@watmath.UUCP (08/25/83)
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) ...!allegra!watmath!ljdickey ...!ucbvax/decvax!watmath!ljdickey University of Waterloo