## An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form.(English)Zbl 0614.65043

For positive definite symmetric matrices $$A_ 1,...,A_ k(k\geq 1)$$ of dimension $$p\times p$$ the measure of simultaneous deviation of $$A_ 1,...,A_ k$$ from diagonality is defined as the function $$\Phi (A_ 1,...,A_ k;\quad n_ 1,...,n_ k)=\prod^{k}_{i=1}[\det (diag A_ i)]^{n_ i}/[\det (A_ i)]^{n_ i}$$ where $$n_ i$$ are positive constants. An algorithm for finding an orthogonal $$p\times p$$ matrix B such that $$\Phi (B^ TA_ 1B,...,B^ TA_ kB;n_ 1,...,n_ k)$$ is minimal is described. Conditions for the uniqueness of the solution are given. For $$k=1$$ the algorithm computes the eigenvectors of the positive definite symmetric matrix. Some examples are shown.
Reviewer: L.Boubeliková

### MSC:

 65F30 Other matrix algorithms (MSC2010) 65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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