Multivariate Procedures Invariant Under Linear Transformations

A note on invariant linear transformations in multivariate public key cryptography

Equations with Constant Coefficients Invariant under a Group of Linear Transformations

If P is a linear differential operator on Rn with constant coefficients, which is invariant under a group G of linear transformations, it is not true in general that the equation Pu = f always has a G-invariant solution u for a G-invariant /. We elucidate here the particular case of a "big" group G, and we count the invariant solutions when they exist (see Corollary 28 and Theorems 32, 33). The...

Adaptive linear procedures under general conditions

Under mild condit ions on the observat ion processes the almost sure convergence propert ies of l inear stochastic approximation are summarized for least squares and for some of its applications: adapt ive filtering, echo cancellation, detection of binary data in Gaussian noise, identification, and linear classification.

Factor analysis invariant to linear transformations of data

Modeling data with Gaussian distributions is an important statistical problem. To obtain robust models one imposes constraints the means and covariances of these distributions [6, 4, 10, 8]. Constrained ML modeling implies the existence of optimal feature spaces where the constraints are more valid [2, 3]. This paper introduces one such constrained ML modeling technique called factor analysis i...

Invariant Measures for Certain Linear Fractional Transformations Mod 1

Explicit invariant measures are derived for a family of finite-toone, ergodic transformations of the unit interval having indifferent periodic orbits. Examples of interesting, non-trivial maps of [0, 1] for which one can readily compute an invariant measure absolutely continuous to Lebesgue measure are not easy to come by. The familiar examples are the Gauss map, the backward continued fraction...