A matrix decomposition theorem

A Martingale Decomposition Theorem

A Cohomology Decomposition Theorem

In [9] Jackowski and McClure gave a homotopy decomposition theorem for the classifying space of a compact Lie group G; their theorem states that for any prime p the space BG can be constructed at p as the homotopy direct limit of a specific diagram involving the classifying spaces of centralizers of elementary abelian p-subgroups of G. In this paper we will prove a parallel algebraic decomposit...

A Decomposition Theorem for Domains

A domain constructor that generalizes the product is de ned. It is shown that with this constructor exactly the prime-algebraic coherent Scott-domains and the empty set can be generated from two-chains and boolean at domains. 3 List of Symbols I am identifying the symbols by the corresponding Latex(+Amssymb)-symbols. " uparrow # downarrow ! rightarrow ? bot > top leq geq 2 in W bigvee V bigwedg...

On Seymour’s Decomposition Theorem

Let M be a class of matroids closed under minors and isomorphism. Let M be a 3-connected matroid in M with an N-minor and let N have an exact k-separation (A, B). If there exists a k-separation (X ,Y ) of M such that A ⊆ X and B ⊆ Y , we say the k-separation (A, B) of N is induced in M. In this paper we give new sufficient conditions to determine if an exact k-separation of N is induced inM.

The Cyclic Decomposition Theorem

Let V be a finite-dimensional F -vector space, and let T : V → V be a linear transformation. In this note we prove that V is a direct sum of cyclic T -invariant subspaces. More specifically, we prove that V is a direct sum of cyclic T -invariant subspaces whose annihilators are generated by powers of irreducible polynomials, and that the collection of these polynomials is uniquely determined. R...