Block lower triangular and block upper triangular matrices are popular preconditioners for nonsymmetric saddle point matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned systems are related. Nonsingular saddle point matrices of the form

The fine spectra of lower triangular double-band matrices were examined by several authors. Here we determine the fine spectra of upper triangular double-band matrices over the sequence spaces () p and () bv p. Upper triangular double-band matrices are infinite matrices which include the left-shift, averaging and difference operators.

Let k be an algebraically closed field. Let B be the Borel subgroup of GLn(k) consisting of nonsingular upper triangular matrices. Let b = LieB be the Lie algebra of upper triangular n × n matrices and u the Lie subalgebra of b consisting of strictly upper triangular matrices. We classify all Lie ideals n of b, satisfying u ⊆ n ⊆ u, such that B acts (by conjugation) on n with a dense orbit. Fur...

Computer memory is linear and contiguous, while the values that enter it are always structured. Typically, is array of ndimensions, upper and lower triangular matrices, or symmetric and skewed symmetric matrices. Functions that map the upper and lower triangular matrices exist in most literatures, however its applications are limited since they cannot handle all order of traversals. This paper ...

The paper considers subspaces of the strictly upper triangular matrices, which are stable under Lie bracket with any matrix. These called ad-nilpotent ideals and there Catalan number such subspaces. Each ideal I meets a unique largest nilpotent orbit OI in algebra all matrices. main result is that an equivalence relation on studied by Mizuno others, classes OI=O for fixed O. We include two appl...