Article

# Determinants of block tridiagonal matrices

Dipartimento di Fisica, Università degli Studi di Milano and INFN, Sezione di Milano, Via Celoria 16, Milano, Italy

Linear Algebra and its Applications 01/2008; DOI: 10.1016/j.laa.2008.06.015 Source: arXiv

- [Show abstract] [Hide abstract]

**ABSTRACT:**The formulas presented in [Molinari, L.G. Determinants of block tridiagonal matri-ces. Linear Algebra Appl., 2008; 429, 2221–2226] for evaluating the determinant of block tridiagonal matrices with (or without) corners are used to derive the determinant of any multidiagonal matri-ces with (or without) corners with some specified non-zero minors. Algorithms for calculation the determinant based on this method are given and properties of the determinants are studied. Some applications are presented.The electronic journal of linear algebra ELA 11/2012; 25:101-117. · 0.89 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Controllable series line compensation is a cornerstone to increase the transmittable power, improve the transient stability and power oscillation damping. The initiative of FACTS allows for fast and vernier control of series compensation using static synchronous series compensator (SSSC). This paper presents the control laws and location index proposed for a SSSC based on a circuit analogy of the electro-mechanical system. The signals which are used can be synthesized using locally available measurements. A detailed study of small signal analysis is carried out to study the effectiveness of the control law and strategic location of the damping controller. With the objective of damping oscillations, a nonlinear constrained optimization technique has been presented for tuning the controller parameters. Transient stability analysis has then been performed with SSSC for a multimachine power system. A path independent structure preserving energy function method (SPEF) is derived for the SSSC. Direct evaluation of the effect of SSSC on transient stability is investigated. Case studies considered illustrate the effect of SSSC on transient stability and its accurate prediction. Comparison of results of the proposed approach with that of the method proposed by M.H. Haque, clearly indicate that there is a good enhancement in the system stability.International Journal of Electrical Power & Energy Systems - INT J ELEC POWER ENERG SYST. 02/2012; - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper presents a method for expressing the determinant of an N {\times} N complex block matrix in terms of its constituent blocks. The result allows one to reduce the determinant of a matrix with N^2 blocks to the product of the determinants of N distinct combinations of single blocks. This procedure proves useful in the analytic description of physical systems with multiple discrete variables, as it provides a systematic method for evaluating determinants which might otherwise be analytically intractable.12/2011;

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.