Algebraic reflexivity of linear transformations

Linear Algebraic Transformations of theBidomain

In this paper we give a mathematical framework for the treatment of the bidomain equations used to model propagation in cardiac tissue. We show how previous work ts into this framework and discuss the implications of various linear transformations of the equations on the numerical methods of solution.

A Linear Algebraic View of Loop Transformations and Their Interaction

Although optimizing transformations have been studied for over two decades, the interactions between them is not well understood. This is particularly important for the success of parallelizing compilers. In order to deal with interactions, we view loop transformations as multiplication by a suitable matrix. The transformations considered are loop interchange, permutation, reversal, hyperplane ...

Algebraic construction of cryptographically good binary linear transformations

MaximumDistance Separable (MDS) andMaximumDistance Binary Linear (MDBL) codes are used as diffusion layers in the design of the well-known block ciphers like the Advanced Encryption Standard, Khazad, Camellia, and ARIA. The reason for the use of these codes in the design of block ciphers is that they provide optimal diffusion effect to meet security of a round function of a block cipher. On the...

On One-Sided Ideals of Rings of Linear Transformations

Algebraic Transformations Ofpolynomial Equations