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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On principal sections of a pair of forms


Author: Che-Man Cheng
Journal: Proc. Amer. Math. Soc. 123 (1995), 2949-2954
MSC: Primary 15A42; Secondary 15A18
MathSciNet review: 1283543
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Abstract: Let H and C be $ n \times n$ Hermitian matrices with C positive definite. Let $ H({i_1}, \ldots ,{i_r})$ denote the submatrix of H formed by deleting the rows and columns $ {i_1}, \ldots ,{i_r}$, of H. In this paper, with $ {r_1} + \cdots + {r_k} \leq n$, we study the roots of the determinantal equation $ \det (\lambda C - H) = 0$ and those of

$\displaystyle \det ((\lambda C - H)({r_1} + \cdots + {r_{i - 1}} + 1, \ldots ,{r_1} + \cdots + {r_i})) = 0$

for $ i = 1, \ldots ,k$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1283543-9
PII: S 0002-9939(1995)1283543-9
Article copyright: © Copyright 1995 American Mathematical Society