We won’t cover: • linear algebra, i.e., the underlying mathematics of matrices • numerical linear algebra, i.e., the algorithms used to manipulate matrices and solve linear equations • software for forming and manipulating matrices, e.g., Matlab, Mathematica, or Octave • how to represent and manipulate matrices, or solve linear equations, in computer languages such as C/C++ or Java • applicatio...

This paper provides a general construction technique for rectangular matrices whose elements are quaternion variables and whose column vectors are formally orthogonal. These matrices are named quaternion orthogonal designs, in parallel with the well-known constructs of real and complex orthogonal designs. The proposed construction technique provides the first infinite family of this type of qua...

Let Hmxn be the set of all m x n matrices over real quaternion algebra. We call that A ? Hnxn is ?-Hermitian if = A?* where -?A*?,? {i,j,k},i,j,k are units. In this paper, we derive some solvability conditions and general solution to a system matrix equations. As an application, present necessary sufficient for existence systems also give expressions solutions these when they solvable. Some num...

These notes describe the notation of matrices, the mechanics of matrix manipulation, and how to use matrices to formulate and solve sets of simultaneous linear equations. We won’t cover • linear algebra, i.e., the underlying mathematics of matrices • numerical linear algebra, i.e., the algorithms used to manipulate matrices and solve linear equations • software for forming and manipulating matr...

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...

In 1988, J.R. Faulkner has given a procedure to construct an octonion algebra on a finite dimensional unitary alternative algebra of degree three over a field K. Here we use a similar procedure to get a quaternion algebra. Then we obtain some conditions for these octonion and quaternion algebras to be split or division algebras. Then we consider the implications of the found conditions to the u...