Rank and Inertia Theorems for Matrices: The Semi-definite Case |
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a₁ Appendix assume b₁ best possible blocks bounds c₁ chapter choose clearly common conformably consider containing Continuing Corollary corresponding d₁ decomposition define H definition determine divisors of degrees elementary divisors equal exists exists a non-singular expansion factors follows given H is non-singular h pq H₁ H₁₁ hence Hermitian iiii illustrate imaginary roots induction inequalities Inertia Theorem integer Lemma linear lower bound Math matrix Method minor obtain P₁ pair partition positive proof proof of Theorem prove rank H rank R(AH Reduction Remark respectively result rows satisfying single singular solution standard notation structure submatrix Suppose term Theorem 4.5 thesis true upper write X X X zero ΣΙΣ