Synthetic aperture radar with polarimetric diversity is a powerful tool in remote sensing. Each pixel described by the scattering matrix corresponding to emission/reception polarization states (usually horizontal and vertical). The algebraic real representation, block symmetric form, introduced adopt more comprehensive framework (non-restricted reciprocity assumptions) mapping consimilarity equ...

Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by finite type string link invariants. For positive string links, the representation matrix can be interpreted as the trans...

Abstract Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a pair of matrix equations. We present a matrix representation of the Maxwell equation in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires 8×8 matrices and...

In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential repres...

In this paper, we introduce the definition of generalized reduced biquaternions and propose a real representation biquaternion matrix. By using matrix representation, discuss least-squares problems classic equation AXC = B. The solution to above is formulated by its corresponding equation. Furthermore, two numerical examples are given illustrate our results.

In mathematics, complete classification of structures, such as groups and rings, is often a primary goal. Linear transformations are no exception to this. Certain canonical forms exist to classify linear transformations, therefore creating a unique representative of linear transformations in the same similarity class. Diagonal representation is of course one of the simplest examples of a canoni...