Joint Approximate Diagonalization of Symmetric Real Matrices of Order 2

Sônia Cristina Poltroniere, Edilaine Martins Soler, Alexys Bruno-Alfonso


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.


Joint approximate diagonalisation; eigenvectors; optimisation.

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