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1	Level Curves of the Angle Function of a Positive Definite Symmetric Matrix Bajracharya, Neeraj 12 1900 (has links) Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix. Jordan product Eigenvalues angle function of a matrix symmetric matrix positive definite matrix level curve Matrices. Curves. Angles (Geometry)
2	Some contributions in probability and statistics of extremes. Kratz, Marie 15 November 2005 (has links) (PDF) Part I - Level crossings and other level functionals.<br />Part II - Some contributions in statistics of extremes and in statistical mechanics. [MATH] Mathematics autoregressive processes chaos decomposition CLT crossings empirical process exceedances extremes Gaussian fileds Gaussian processes heavy tails Hermite polynomials level curve level functionals linear programming maxima moving average processes order statistics parameter estimation Poisson convergence Poisson processes qq-plot random spin systems rate of convergence regular variation sojourn time spectral moment Stein-Chen method time series analysis

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Level Curves of the Angle Function of a Positive Definite Symmetric Matrix

Some contributions in probability and statistics of extremes.