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 Waterlooljdickey@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
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University of Waterloo