Newsgroups: sci.math
From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: Fri, 24 Sep 1993 21:05:39 GMT
Subject: Re: Q: Row,col of element in upper T matrix?

j...@cac.psu.edu (JAMES J VINCENT) asks:

> Can anyone suggest a straightforward way to determine the row and
> column number of a given element of a matrix while only counting
> elements of the upper triangle, including the diagonal? For instance
> in a 6x6 matrix if I want the 8th element it would be row 2, column 3
> by counting across rows, and only counting the upper triangle members.

In an NxN matrix, if the I'th element is Row R, Column C, then

  I = (R-1)(2N-R+2)/2 + (C-R+1)

The inverse is given as

  R = N - floor((sqrt((2N+1)^2 - 8I + 4) - 1)/2)

  C = I - (2N-R)(R-1)/2

Be sure to credit your sources.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil