THE MOORE-PENROSE INVERSE OF THE RECTANGULAR FIBONACCI MATRIX AND APPLICATIONS TO THE CRYPTOLOGY

Abstract

In this paper, we define the general form of the Moore-Penrose inverse for the matrix whose elements are Fibonacci numbers. We examine the states of the matrix $F \in M_{m, n}(\mathbb{C})$, where $F$ is a rectangular Fibonacci matrix based on the values of $m$ and $n$. In the second part of this study, we introduce a novel coding theory using the MoorePenrose inverse of the rectangular Fibonacci matrix and provide illustrative examples. The rectangular Fibonacci matrix plays a crucial role in the construction of the coding algorithm. This coding method is referred to as the "coding theory on rectangular Fibonacci matrix." Received: August 12, 2023Accepted: October 19, 2023

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