Quaternionic Hamilton equations
نویسنده
چکیده
The classical Hamilton equations are reinterpreted by means of complex analysis, in a non standard way. This suggests a natural extension of the Hamilton equations to the quaternionic case, extension which coincides with the one introduced in [1] by a completely different approach.
منابع مشابه
2000]30g35, 70h05 Quaternionic Hamilton Equations
The classical Hamilton equations are reinterpreted by means of complex analysis, in a non standard way. This suggests a natural extension of the Hamilton equations to the quaternionic case, extension which coincides with the one introduced in [2] by a completely different approach.
متن کاملOn Positive Definite Solutions of Quaternionic Matrix Equations
The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established. Keywords...
متن کاملA Brief History of Quaternions and the Theory of Holomorphic Functions of Quaternionic Variables
In this paper I will give a brief history of the discovery (Hamilton, 1843) of quaternions. I will address the issue of why a Theory of Triplets (the original goal of Hamilton) could not be developed. Finally, I will discuss briey the history of various attempts to de ne holomorphic functions on quaternionic variables. Advised By Daniele C. Struppa, Ph.D. Chancellor Chapman University One Univ...
متن کاملSome Inequalities for Sums of Nonnegative Definite Matrices in Quaternions
The collection of all quaternions is denoted byH and is called the real quaternionic algebra. This algebra was first introduced by Hamilton in 1843 (see [5, 6]), and is often called the Hamilton quaternionic algebra. It is well known thatH is an associative division algebra over R. For any a= a0 + a1i+ a2 j + a3k ∈H, the conjugate of a = a0 + a1i + a2 j + a3k is defined to be a = a0 − a1i− a2 j...
متن کاملQuaternionic Monge-ampère Equations
The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in H. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].
متن کامل