On Systems of Linear Quaternion Functions

نویسنده

  • Todd A. Ell
چکیده

A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under functional composition. Furthermore, the composition operation is symbolically identical to quaternion multiplication, making manipulation and reduction of systems of linear quaternion functions straight forward.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

متن کامل

Some results on higher numerical ranges and radii of quaternion matrices

‎Let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $A$ be an $n$-square quaternion matrix‎. ‎In this paper‎, ‎some results on the $k-$numerical range of $A$ are investigated‎. ‎Moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $A$ are introduced‎, ‎and some of their algebraic properties are studied‎.

متن کامل

High-Performance Robust Three-Axis Finite-Time Attitude Control Approach Incorporating Quaternion Based Estimation Scheme to Overactuated Spacecraft

With a focus on investigations in the area of overactuated spacecraft, a new high-performance robust three-axis finite-time attitude control approach, which is organized in connection with the quaternion based estimation scheme is proposed in the present research with respect to state-of-the-art. The approach proposed here is realized based upon double closed loops to deal with the angular rate...

متن کامل

Numerical solution of linear control systems using interpolation scaling functions

The current paper proposes a technique for the numerical solution of linear control systems.The method is based on Galerkin method, which uses the interpolating scaling functions. For a highly accurate connection between functions and their derivatives, an operational matrix for the derivatives is established to reduce the problem to a set of algebraic equations. Several test problems are given...

متن کامل

A NOTE ON EVALUATION OF FUZZY LINEAR REGRESSION MODELS BY COMPARING MEMBERSHIP FUNCTIONS

Kim and Bishu (Fuzzy Sets and Systems 100 (1998) 343-352) proposeda modification of fuzzy linear regression analysis. Their modificationis based on a criterion of minimizing the difference of the fuzzy membershipvalues between the observed and estimated fuzzy numbers. We show that theirmethod often does not find acceptable fuzzy linear regression coefficients andto overcome this shortcoming, pr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008