Open AccessJoint Approximate Diagonalization of Symmetric Real Matrices of Order 2
Author(s) -
Sônia Cristina Poltroniere,
Edilaine Martins Soler,
Alexys Bruno-Alfonso
Publication year - 2016
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2016.017.01.0113
Subject(s) - eigenvalues and eigenvectors , matrix similarity , orthogonal matrix , matrix (chemical analysis) , mathematics , transformation (genetics) , interpretation (philosophy) , diagonalizable matrix , orthogonal transformation , symmetric matrix , normal matrix , computer science , algorithm , orthogonal basis , mathematical analysis , physics , biochemistry , chemistry , materials science , quantum mechanics , partial differential equation , composite material , gene , programming language
The problem of joint approximate diagonalization of symmetric real matrices is addressed. It is reduced to an optimization problem with the restriction that the matrix of the similarity transformation is orthogonal. Analytical solutions are derived for the case of matrices of order 2. The concepts of off-diagonalising vectors, matrix amplitude and partially complementary matrices are introduced. This leads to a geometrical interpretation of the joint approximate diagonalization in terms of eigenvectors and off-diagonalising vectors of the matrices. This should be helpful to deal with numerical and computational procedures involving large matrices.