In multivariate statistical analysis. orthogonally invariant sets of real positive definite pxp matrices occur as acceptance regions for tests of invariant hypotheses concerning the covariance matrix [ of a multivariate normal distribution. Equivalently. orthogonally invariant acceptance regions can be expressed in terms of the eigenvalues I, (S). .... lp(S) of a random Wishart matrix S Wp(n. [...

We unify and generalize several known results about systems of random polynomials. We first classify all orthogonally invariant normal measures for spaces of polynomial mappings. For each such measure we calculate the expected number of real zeros. The results for invariant measures extend to underdetermined systems, giving the expected volume for orthogonally invariant random real projective v...

Abstract Let q be a nondegenerate quadratic form on V . X ⊂ invariant for the action of Lie group G contained in S O ( , ). For any f ∈ consider function d from to $\mathbb C$ ℂ defined by x ) = − We show that critical points lie subspace orthogonal ${\mathfrak g}\cdot f$ g ⋅...

1992 Abstract We present a new method of multi-resolution image analysis that gives us the most concise set of local orthogonally invariant features of 2-dimensional input images. Solving the equivalence problem corresponding to a local jet and the group of orthogonal transformations of the cartesian coordinate frame we nd a complete and irreducible set of local algebraic invariants that may de...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of randommatrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two bounded derivatives.