Abstract

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20 Matrix Theory-Applications and Theorems

1081-3810.1635

laa.2003.12.039

We introduce and study a matrix which has the exponential function as one of its eigenvectors. We realize that this matrix represents a set of finite differences derivation of vectors on a partition. This matrix leads to new expressions for finite differences derivatives which are exact for the exponential function. We find some properties of this matrix, the induced derivatives and of its inverse. We provide an expression for the derivative of a product, of a ratio, of the inverse of vectors, and we also find the equivalent of the summation by parts theorem of continuous functions. This matrix could be of interest to discrete quantum mechanics theory.

Keywords: exact finite differences derivative, exact derivatives on partitions, exponential function on a partition, discrete quantum mechanics
