A generalization of the matrix-tree theorem
β Scribed by Mordechai Lewin
- Publisher
- Springer-Verlag
- Year
- 1982
- Tongue
- French
- Weight
- 750 KB
- Volume
- 181
- Category
- Article
- ISSN
- 0025-5874
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The 'All Minors Matrix Tree Theorem' (Chen, Applied Graph Theory, Graphs and Electrical Networks, North-Holland, Amsterdam, 1976; Chaiken, SIAM J. Algebraic Discrete Math. 3 (3) (1982) 319-329) is an extension of the well-known 'Matrix Tree Theorem' (Tutte, Proc. Cambridge Philos. Sot. 44 (1948) 463
We show that the inertia of a quadratic matrix polynomial is determined in terms of the inertia of its coefficient matrices if the leading coefficient is Hermitian and nonsingular, the constant term is Hermitian, and the real part of the coefficient matrix of the first degree term is definite. In pa