Inertia theory for simultaneously triangulable complex matrices
نویسندگان
چکیده
منابع مشابه
Perron-frobenius Theory for Complex Matrices
The purpose of this paper is to present a unified Perron-Frobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The sign-real spectral radius was introduced for general real matrices. This quantity was shown to share certain properties with the Perron root of nonnegative matrices. In this paper we introduce the sign-complex spectral radius. Agai...
متن کاملA Theory of Matrices of Complex Elements
The articles [11], [14], [1], [4], [2], [15], [6], [10], [9], [3], [8], [7], [13], [12], and [5] provide the terminology and notation for this paper. The following two propositions are true: (1) 1 = 1CF . (2) 0CF = 0. Let A be a matrix over C. The functor ACF yields a matrix over CF and is defined by: (Def. 1) ACF = A. Let A be a matrix over CF. The functor AC yielding a matrix over C is define...
متن کاملThe Inertia of Hermitian Tridiagonal Block Matrices
Let H be a partitioned tridiagonal Hermitian matrix. We characterized the possible inertias of H by a system of linear inequalities involving the orders of the blocks, the inertia of the diagonal blocks and the ranks the lower and upper subdiagonal blocks. From the main result can be derived some propositions on inertia sets of some symmetric sign pattern matrices.
متن کاملInertia Theorems for Matrices: the Semi-definite Case
1. The inertia of a square matrix A with complex elements is defined to be the integer triple In A = (ir(A), V(A), 8(4)), where ir(A) {v(A)} equals the number of eigenvalues in the open right {left} half plane, and 8(A) equals the number of eigenvalues on the imaginary axis. The best known classical inertia theorem is that of Sylvester : If P > 0 (positive definite) and H is Hermitian, then In ...
متن کاملApproximation Theory for Matrices
There are many situations in which it is desirable to evaluate a function of a matrix. For instance, in lattice quantum field theory it is sometimes desirable to evaluate the square root of a discretised Dirac operator D/ in order to calculate the effects of varying the number of fermionic flavours [1,2,3,4,5], or to construct a good approximation to Neuberger’s operator for GinspargWilson ferm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1969
ISSN: 0024-3795
DOI: 10.1016/0024-3795(69)90022-6