About: Haynsworth inertia additivity formula

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In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth (1916–1985), concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it is partitioned. The inertia of a Hermitian matrix H is defined as the ordered triple whose components are respectively the numbers of positive, negative, and zero eigenvalues of H. Haynsworth considered a partitioned Hermitian matrix where H11 is nonsingular and H12* is the conjugate transpose of H12. The formula states:

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  • In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth (1916–1985), concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it is partitioned. The inertia of a Hermitian matrix H is defined as the ordered triple whose components are respectively the numbers of positive, negative, and zero eigenvalues of H. Haynsworth considered a partitioned Hermitian matrix where H11 is nonsingular and H12* is the conjugate transpose of H12. The formula states: where H/H11 is the Schur complement of H11 in H: (en)
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  • In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth (1916–1985), concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it is partitioned. The inertia of a Hermitian matrix H is defined as the ordered triple whose components are respectively the numbers of positive, negative, and zero eigenvalues of H. Haynsworth considered a partitioned Hermitian matrix where H11 is nonsingular and H12* is the conjugate transpose of H12. The formula states: (en)
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  • Haynsworth inertia additivity formula (en)
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