Diagonalization in Jordan pairs

Jordan forms for mutually annihilating nilpotent pairs

We consider pairs of n × n commuting matrices over an algebraically closed field F . For n, a, b (all at least 2) let V(n, a, b) be the variety of all pairs (A,B) of commuting nilpotent matrices such that AB = BA = A = B = 0. In [14] Schröer classified the irreducible components of V(n, a, b) and thus answered a question stated by Kraft [9, p. 201] (see also [3] and [10]). If μ = (μ1, μ2, . . ....

Approximation of Jordan homomorphisms in Jordan Banach algebras RETRACTED PAPER

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation begin{align*} sum_{k=2}^n sum_{i_1=2}^ksum_{i_2=i_{1}+1}^{k+1}cdotssum_{i_n-k+1=i_{n-k}+1}^n fleft(sum_{i=1,i not=i_{1},cdots ,i_{n-k+1}}^n x_{i}-sum_{r=1}^{n-k+1} x_{i_{r}}right) + fleft(sum_{i=1}^{n}x_{i}right)-2^{n-1} f(x_{1}) =0, end{align*} where ...

Diagonalization methods in PARSEC ∗

The Pseudopotential Algorithm for Real-Space Electronic Calculations (PARSEC) is a software package written by a team consisting of materials scientists and computer scientists over approximately one decade. During this period, the algorithms used in PARSEC have undergone a series of improvements. This paper reviews the nature of the eigenvalue problems encountered in solving the Kohn-Sham equa...

Diagonalization in Parallel Space

Matrix diagonalization is an important component of many aspects of computational science. There are a variety of algorithms to accomplish this task. Jacobi’s algorithm is a good choice for parallel environments. Jacobi’s algorithm consists of a series of matrix plane rotations, the ordering of which can dramatically affect performance. We show a new ordering which cuts the number of necessary ...

Diagonalization in proof complexity