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Maximum and minimum problems in functions of quadratic forms

1957

Let A be an n x n hermitian matrix, let E₂(a₁, ..., a_k) be the second elementary symmetric function of the letters a₁, ..., a_k and let C₂(A) be the second compound matrix of A. In this thesis the maximum and minimum of det {(Ax_█, x_j)} and E₂ [(Ax₁, x₁), ..., (Ax_█(k@), x_k)] the minimum of [formula omitted] (C₂(A)x_i ₁⋀x_i₂ , x_i₁ ⋀ax_i₂) are calculated. The maxima and minima are taken over all sets of k orthonormal vectors in unitary n-space and x_█(i@)₁ ⋀ x_i ₂ designates the Grassman

doi:10.14288/1.0080646
fatcat:c66c35ea6vayvnusqi6zct65zm