The structure of matrices that represent a linear transformation of the Stokes parameters of a beam of light into the Stokes parameters of another beam of light is investigated by means of the so-called Stokes criterion. This holds that the degree of polarization of a beam of light can never be changed into a number larger than unity. Several general properties are derived for matrices satisfyi...

We introduce two new sets of invariant functions of quark mass matrices, which express the constraints on these mass matrices due to knowledge of the quark mixing matrix. These invariants provide a very simple method to test candidate forms for mass matrices. Supported in part by NSF contract PHY-89-08495 email: [email protected] In recent years the increasingly accurate data on quark mix...

We propose to use a new feature transformation (FT) function to construct supervectors of support vector machines for speaker recognition. Considering that estimation of bias vectors is more robust than that of transformation matrices, we define the FT function in a flexible form that transformation matrices and bias vectors are controlled by separate regression classes. Unlike the MLLR-based a...

Many emerging applications formulate nonpositive semidefinite similarity matrices, and hence cannot fit into the framework of kernel machines. A popular approach to this problem is to transform the spectrum of the similarity matrix so as to generate a positive semidefinite kernel matrix. In this paper, we present an analytical framework to explore four representative transformation methods: den...

The P -property of the following two Z-transformations with respect to the positive semidefinite cone is characterized: (i) I − S, where S : S → S is a nilpotent linear transformation, (ii) I − L A , where LA is the Lyapunov transformation defined on S n×n by LA(X) = AX + XA . (Here S denotes the space of all symmetric n×n matrices and I is the identity transformation.)