Notes on the matrix exponential
نویسنده
چکیده
The purpose of these notes is to describe how one can compute the matrix exponential e when A is not diagonalisable. This is done in Teschl by transforming A into Jordan normal form. As we will see here, it is not necessary to go this far. It su ces to transform A into block form, where each block only has one eigenvalue (up to multiplicity). For completeness we also present a proof of the Jordan normal form at the end. The material in these notes is roughly the same as in Chapter 3.8 of Teschl, but the presentation and the proofs are a bit di erent. We also give more examples.
منابع مشابه
Some notes on the characterization of two dimensional skew cyclic codes
A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code. It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$. In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...
متن کاملThe exponential functions of central-symmetric $X$-form matrices
It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $X$-form. For instance, $e^{mathbf{A}t}$, $t^{mathbf{A}}$ and $a^{mathbf{A}t}$ will be evaluated by the new formulas in this par...
متن کاملDominating Sets in Circulant Graphs
We give an efficient construction of a reasonably small dominating set in a circulant graph on n notes and k distinct chord lengths. This result is based on bounds on some double exponential sums.
متن کاملOn Exponential Power Distribution And Poultry Feeds Data: A Case Study
Abstract. In this paper, we propose to study a generalized form of the exponential power distribution which contains others in the literature as special cases. This unifying exponential power distribution is characterized by a parameter ω and a function h(ω) which regulates the tail behavior of the distribution, thus making it more flexible and suitable for modeling than the usual normal di...
متن کاملSolving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...
متن کامل