In this paper, we investigate a system of twelve quaternion matrix equations. Using the real representation matrix, first derive least-squares solution with least norm to system. Meanwhile, establish solvability conditions and an expression general when it is consistent.

Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green, and blue channels of images. A low-rank approximation for obtained by using the singular value decomposition. However, this is not optimal sense that resulting may quaternion, i.e., contains real component which useful representa...

Three-dimensional coordinate transformation problem is the most frequent problem in photogrammetry, geodesy, mapping, geographical information science (GIS), and computer vision. To overcome the drawback that traditional solution of the problem based on rotation angles depends strongly on initial value of parameter, which makes the method ineffective in the case of super-large rotation angle, t...

The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared for its importance with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science.-Clerk Maxwell, 1869. Quaternions came from Hamil...

The practical and accurate computation of the singular value decomposition of a quaternion matrix is of importance in vector signal processing using quaternions. We present a Jacobi algorithm for computing such an SVD, and discuss its utility and accuracy. The algorithm is included in an open-source Matlab toolbox for quaternions where it serves as an accurate reference implementation.

A variety of universal similarity factorization equalities over real Clifford algebras Rp,q are established. On the basis of these equalities, real, complex and quaternion matrix representations of elements in Rp,q can be explicitly determined.

Palmprints have been widely studied for biometric recognition for many years. Traditionally, a white light source is used for illumination. Recently, multispectral imaging has drawn attention because of its high recognition accuracy. Multispectral palmprint systems can provide more discriminant information under different illuminations in a short time, thus they can achieve better recognition a...

A necessary and sufficient condition is given for the quaternion matrix equations AiX + Y Bi = Ci (i = 1, 2) to have a pair of common solutions X and Y . As a consequence, the results partially answer a question posed by Y.H. Liu (Y.H. Liu, Ranks of solutions of the linear matrix equation AX + Y B = C, Comput. Math. Appl., 52 (2006), pp. 861-872).

The main purpose of this paper is to show the application of mathematical system of quaternions in physics. We show a basic way of generating a quaternion operator and a method of obtaining the Schrodinger’s equation using this operator matrix. Then we investigate the various probable uses of the coefficient matrix to scale relativity and spacetime quantization.