In this paper we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise. We derive the generalized likelihood ratio (GLR) for each problem in the class. We then establish the invariances for the GLR and argue that these are the natural invariances for the problem. In each case, the GLR is a maximal invariant statistic, and the distribut...

The famous Lomonosov’s invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E “commutes” with a compact operator K 6= 0, i.e., TK = KT, then T has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators. We also provide some applications to singlevalued linear operators.

We present an overview of the banded Invariant Subspace Decomposition Algorithm for symmetric matrices and describe a parallel implementation of this algorithm. The algorithm described here is a promising variant of the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA) that retains the property of using scalable primitives, while requiring signiicantly less overal...

Given the set of matrix pairs M ⊂ Mm,n(C) × Mn(C) keeping a subspace S ⊂ C invariant, we obtain a miniversal deformation of a pair belonging to an open dense subset of M. It generalizes the known results when S is a supplementary subspace of the unobservable one. Keywords-Conditioned invariant subspaces, Miniversal deformation, Stratified manifold, Vertical pairs of matrices.