M. L. Pei [Comm. ACM 5, 10 (Oct. 1962)] gave an explicit inverse for a matrix of the form M + &dgr;I, where M is an n-square matrix of ones and &dgr; is a nonzero parameter. The eigenvalues of the Pei matrix were given by W. S. LaSor [Comm. ACM 6, 3 (Mar. 1963)]. The eigenvectors may be obtained by considering the system (M+&dgrI)x = &lgr;x, the jth equation of which is S + &dgr;xj = &lgr;xj , (1) where S denotes ∑ni=1 xi. On summing the equations for j = 1, 2, ··· , n, we obtain nS + &dgr;S = &lgr;S. From this we conclude that (a) S = 0 or (b) &lgr; = n + &dgr;.
The full text of this article is premium content
No entries found
Log in to Read the Full Article
Please select one of the options below for access to premium content and features.
Create a Web Account
If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.
Join the ACM
Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.
Subscribe to Communications of the ACM Magazine
Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.
Purchase the Article
Non-members can purchase this article or a copy of the magazine in which it appears.