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 Hermitian matrices with *C* positive definite. Let denote the submatrix of *H* formed by deleting the rows and columns , of *H*. In this paper, with , we study the roots of the determinantal equation and those of

**[1]**Che-Man Cheng,*Independence of eigenvalues and independence of singular values of submatrices*, Linear Algebra Appl.**166**(1992), 115–129. MR**1152490**, 10.1016/0024-3795(92)90272-C**[2]**Ky Fan and Gordon Pall,*Imbedding conditions for Hermitian and normal matrices*, Canad. J. Math.**9**(1957), 298–304. MR**0085216****[3]**Roger A. Horn and Charles R. Johnson,*Matrix analysis*, Cambridge University Press, Cambridge, 1990. Corrected reprint of the 1985 original. MR**1084815****[4]**Chi-Kwong Li,*Matrices with some extremal properties*, Linear Algebra Appl.**101**(1988), 255–267. MR**941306**, 10.1016/0024-3795(88)90153-X**[5]**R. C. Thompson,*Principal submatrices. IV. On the independence of the eigenvalues of different principal submatrices*, Linear Algebra and Appl.**2**(1969), 355–374. MR**0245601****[6]**R. C. Thompson,*Principal submatrices. VIII. Principal sections of a pair of forms*, Rocky Mountain J. Math.**2**(1972), no. 1, 97–110. MR**0294362**

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1283543-9

Article copyright:
© Copyright 1995
American Mathematical Society