منابع مشابه
The quaternionic determinant
The determinant for complex matrices cannot be extended to quaternionic matrices. Instead, the Study determinant and the closely related q-determinant are widely used. We show that the Study determinant can be characterized as the unique functional which extends the absolute value of the complex determinant and discuss its spectral and linear algebraic aspects. 1. Introduction. Quaternionic lin...
متن کاملQuaternionic Matrices: Inversion and Determinant ∗
We discuss the Schur complement formula for quaternionic matrices, M , and give an efficient method to calculate the matrix inverse. We also introduce the functional D[M ] which extends to quaternionic matrices the non-negative number |det[M ]|. 1. Introduction. Much of the spectral theory of complex matrices does not extend to quaternion matrices without further modifications [1, 2, 3]. In par...
متن کاملOn the determinant of quaternionic polynomial matrices and its application to system stability
The research reported in this paper is motivated by the study of stability for linear dynamical systems with quaternionic coefficients. These systems can be used to model several physical phenomena, for instance, in areas such as robotics and quantum mechanics. More concretely, quaternions are a powerful tool in the description of rotations [1]. There are situations, especially in robotics, whe...
متن کاملdeterminant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
15 صفحه اولQuaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal deformations sending the standard flat torsion-free quaternionic contac...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2000
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1050