ENGINEERING:LINEAR ALGEBRA FOR DATA ANALYSIS: PART2 Single value decomposition A eigenvalue matrix can be decomposed into three matrices ,which represent two rotation of the vector and one scaling. A= P.V.Pinverse A square ,symmetrical matrix can also be decomposed by a different method called single value decomposition. Suppose we have a circle with orthogonal radiii as vectors ,v1 and v2. If we stretch the circle into an ellipse these vectors change into new vectors , the major and minor axis.To allow this transformation of vectors the angle between them has to be orthogonal. Also the stretching can be incorporated by a scaling factor when the norm of the vector remains unchanged during the transformation. These properties occur in orthonormal matrices. So the transformation of radii vectors can be represented by A. v= sigma. u. Here u matrix is called Principal Axis and sigma or scaling factor is called single value. wh...