# zbMATH — the first resource for mathematics

Remarks on inertia theorems for matrices. (English) Zbl 0344.15008

##### MSC:
 15A18 Eigenvalues, singular values, and eigenvectors 15A24 Matrix equations and identities 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
Full Text:
##### References:
 [1] D. Carlson, H. Schneider: Inertia theorems for matrices: The semidefinite case. J. Math. Anal. Appl. 6 (1963), 430-446. · Zbl 0192.13402 [2] Ch.-T. Chen: A generalisation of the inertia theorem. SIAM J. Appl. Math. 25 (1973), 158-161. · Zbl 0273.15009 [3] R. D. Hill: Inertia theory for simultaneously triangulable complex matrices. Linear Algebra Appl. 2 (1969), 131-142. · Zbl 0186.33901 [4] A. Ostrowski, H. Schneider: Some theorems on the inertia of general matrices. J. Math. Anal. Appl. 4 (1962), 72-84. · Zbl 0112.01401 [5] R. A. Smith: Bounds for quadratic Lyapunov functions. J. Math. Anal. Appl. 12 (1965), 425-435. · Zbl 0135.29802 [6] R. A. Smith: Matrix calculations for Lyapunov quadratic forms. J. Diff. Equations 2 (1966), 208-217. · Zbl 0151.02206 [7] [7J O. Taussky: A generalization of a theorem by Lyapunov. J. Soc. Ind. Appl. Math. 9 (1961), 640-643. · Zbl 0108.01202 [8] O. Taussky: Matrices $$C$$ with $$C^{n}\rightarrow 0$$. J. Algebra / (1964), 5-10. · Zbl 0288.15015 [9] H. K. Wimmer: Inertia theorems for matrices, controllability and linear vibrations. Linear Algebra Appl. 8 (1974), 337-343. · Zbl 0288.15015 [10] H. K. Wimmer: An inertia theorem for tridiagonal matrices and a criterion of Wall on continued fractions. Linear Algebra Appl. 9 (1974), 41 - 44. · Zbl 0294.15009 [11] A. D. Ziebur: On determining the structure of A by analysing $$e^At$$. SIAM Review 12 (1970), 98-102. · Zbl 0192.37003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.