Pseudo-Linear Transformations

Pseudo linear transformations and evaluation in Ore extensions

The relations between evaluation of Ore polynomials and pseudo-linear transformations are studied. The behavior of these transformations under homomorphisms of Ore extensions, in particular with respect to algebraicity, is analyzed leading to characterization of left and right primitivity of an Ore extension. Necessary and sufficient conditions are given for algebraic pseudo-linear transformati...

Linear Transformations

The n×m matrix AT obtained by exchanging rows and columns of A is called the transpose of A. A matrix A is said to be symmetric if A = AT . The sum of two matrices of equal size is the matrix of the entry-by-entry sums, and the scalar product of a real number a and an m× n matrix A is the m× n matrix of all the entries of A, each multiplied by a. The difference of two matrices of equal size A a...

Conformal Transformations of Pseudo-Rie- mannian manifolds

This is a survey about conformal mappings between pseudo-Riemannian manifolds and, in particular, conformal vector fields defined on such. Mathematics Subject Classification (2000). Primary 53C50; Secondary 53A30; 83C20.

On One-Sided Ideals of Rings of Linear Transformations

Learning Linear Transformations

We present a polynomial time algorithm to learn (in Valiant's PAC model) cubes in n? space (with general sides-not necessarily axes parallel) given uniformly distributed samples from the cube. In fact, we solve a more general problem of learning in polynomial time linear transformations in n?space. I.e., suppose x is an n?vector whose coordinates are mutually independent random variables with u...