Skip to main content
placeholder image

On orthogonal matrices with constant diagonal

Journal Article


Abstract


  • In connection with the problem of finding the best projections of k-dimensional spaces embedded in n-dimensional spaces Hermann König asked: Given m∈R and n∈N, are there n×n matrices C=(cij), i, j=1,...,n, such that cii=m for all i, |cij|=1 for i≠j, and C2=(m2+n-1)In? König was especially interested in symmetric C, and we find some families of matrices satisfying this condition. We also find some families of matrices satisfying the less restrictive condition CCT=(m2+n-1)In. © 1982.

Publication Date


  • 1982

Citation


  • On orthogonal matrices with constant diagonal (1982). Linear Algebra and Its Applications, 46(C), 117-129. doi:10.1016/0024-3795(82)90031-3

Scopus Eid


  • 2-s2.0-49049135023

Web Of Science Accession Number


Start Page


  • 117

End Page


  • 129

Volume


  • 46

Issue


  • C

Abstract


  • In connection with the problem of finding the best projections of k-dimensional spaces embedded in n-dimensional spaces Hermann König asked: Given m∈R and n∈N, are there n×n matrices C=(cij), i, j=1,...,n, such that cii=m for all i, |cij|=1 for i≠j, and C2=(m2+n-1)In? König was especially interested in symmetric C, and we find some families of matrices satisfying this condition. We also find some families of matrices satisfying the less restrictive condition CCT=(m2+n-1)In. © 1982.

Publication Date


  • 1982

Citation


  • On orthogonal matrices with constant diagonal (1982). Linear Algebra and Its Applications, 46(C), 117-129. doi:10.1016/0024-3795(82)90031-3

Scopus Eid


  • 2-s2.0-49049135023

Web Of Science Accession Number


Start Page


  • 117

End Page


  • 129

Volume


  • 46

Issue


  • C