On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

Download or read book On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices written by Hamiyet Merkepçi and published by Infinite Study. This book was released on 2023-01-01 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. In this research, we will find easy-to-use algorithms for calculating the determinant of a symbolic 3-plithogenic/4-plithogenic matrix, and for finding its inverse based on its classical components, and even for diagonalizing matrices of these types. On the other hand, we will present a new algorithm for calculating the eigenvalues an eigenvectors associated with matrices of these types. Also, the exponent of symbolic 3-plithogenic and 4-plithogenic real matrices will be presented, with many examples to clarify the novelty of this work.