Open AccessGENERALIZATION OF “A THEOREM CONCERNING THE REARRANGEMENTS OF TWO SETS” 1
Author(s) -
Kristof Walter
Publication year - 1969
Publication title -
ets research bulletin series
Language(s) - English
Resource type - Journals
eISSN - 2333-8504
pISSN - 0424-6144
DOI - 10.1002/j.2333-8504.1969.tb00764.x
Subject(s) - transpose , hermitian matrix , generalization , mathematics , simple (philosophy) , matrix (chemical analysis) , diagonal , unitary state , pure mathematics , unitary matrix , combinatorics , function (biology) , group (periodic table) , matrix function , range (aeronautics) , diagonal matrix , algebra over a field , discrete mathematics , symmetric matrix , mathematical analysis , physics , geometry , eigenvalues and eigenvectors , philosophy , materials science , epistemology , quantum mechanics , evolutionary biology , political science , law , composite material , biology
The range of the function tr ZΓZ*Δ is determined when Γ and Δ are real diagonal matrices and matrix Z with hermitian transpose Z * varies unrestrictedly over the group of unitary matrices. Two equivalent versions of the result are given. The real case ( Z restricted to be real orthogonal) is considered separately. Further specialization of the matrix argument yields a “very simple, but important,” theorem on rearrangements of two finite sets of real numbers. Two applications are appended by way of illustration.