eJMT Abstract

Title Matrix decomposition by transforming the unit sphere to an Ellipsoid through Dilation, Rotation and Shearing
Author Wei-Chi YANG and AmirHosein SADEGHIMANESH
Volume 16
Number 3

There are various decompositions of matrices in the literature such as lower-upper, singular value and polar decompositions to name a few. In this paper we are concerned with a less standard matrix decomposition for invertible matrices of order 3 with real entries, called TRD decomposition. In this decomposition an invertible matrix is written as product of three matrices corresponding to a shear, a rotation and a dilation map that transform the unit sphere to an ellipsoid. The reason of our interest is the geometric visualization of this decomposition. We also implemented an algorithm to compute this decomposition both in Maple and Matlab.