In this short note we report on invariant subspaces in Simpira in the case of four registers. In particular, we show that the whole input space (respectively output space) can be partitioned into invariant cosets of dimension 56 over F 28 . These invariant subspaces are found by exploiting the non-invariant subspace properties of AES together with the particular choice of Feistel configuration....

Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...

Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...

The main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. The methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [B. R. Yahaghi, Near triangularizability implies triangularizability, Canad. Math. Bull. 47, (2004), no. 2...

Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some ...

The invariant subspace method is used to classify a class of systems of nonlinear dispersive evolution equations and determine their invariant subspaces and exact solutions. A crucial step is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that systems of evolution equations admit. A few examples of presenting exact solutions with generalized sepa...