Abstract: In this paper, we consider the skew circulant and skew left circulant matrices with the Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices are also discussed. We obtain the determ...

Transformation matrices between different coupling schemes are required, if a reliable classification of the level structure is to be obtained for open–shell atoms and ions. While, for instance, relativistic computations are traditionally carried out in jj−coupling, a LSJ coupling notation often occurs much more appropriate for classifying the valence–shell structure of atoms. Apart from the (k...

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. We show that the Fast Givens transformation, known for the real case, can also be defined for quaternion valued matrices, and we apply this technique to the r...

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. We show that the Fast Givens transformation, known for the real case, can also be defined for quaternion valued matrices, and we apply this technique to the r...

In this paper, a perceptual color difference is presented as an alternative color difference metric for complex images instead of the conventional color difference equations. This color difference is derived based on Mahalanobis distance by using covariance matrices for differences of each color attributes. The covariance matrices for each class of images can be obtained by psychophysical exper...