Right Eigenvalues for Quaternionic Matrices: a Topological Approach
نویسنده
چکیده
We apply the Lefschetz Fixed Point Theorem to show that every square matrix over the quaternions has right eigenvalues. We classify them and discuss some of their properties such as an analogue of Jordan canonical form and diagonalization of elements of the compact symplectic group Sp(n).
منابع مشابه
Localization theorems for eigenvalues of quaternionic matrices
Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix. We see that the above theorems for the left eigenvalues are also true for the case of right eigenvalues, when the diagonals of quaternionic matrix are real. Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the ...
متن کاملA mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...
متن کاملLocation for the Left Eigenvalues of Quaternionic Matrix
The purpose of this paper is to locate and estimate the left eigenvalues of quaternionic matrices. We present some distribution theorems for the left eigenvalues of square quaternionic matrices based on the generalized Gerschgorin theorem and generalized Brauer theorem.
متن کاملRandom right eigenvalues of Gaussian quaternionic matrices
We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance 1/n. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension n goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on mo...
متن کاملQuaternionic quantum walks of Szegedy type and zeta functions of graphs
We define a quaternionic extension of the Szegedy walk on a graph and study its right spectral properties. The condition for the transition matrix of the quaternionic Szegedy walk on a graph to be quaternionic unitary is given. In order to derive the spectral mapping theorem for the quaternionic Szegedy walk, we derive a quaternionic extension of the determinant expression of the second weighte...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999