Understanding the Concept of S adjacent k-sparse Matrices

S adjacent k-sparse matrices (SKMs) are a type of matrix of interest in numerous applications in signal processing, data analytics, and network science. In this text, we will discuss the concept and importance of SKMs in mathematical computing.

Introduction

S adjacent k-sparse matrices are a type of matrix that is used in various signal processing applications. The matrix has a unique characteristic of sparsity, which is an important property in several applications. Sparsity refers to the number of non-zero elements in a matrix. In SKMs, the non-zero elements are placed on the diagonal of the matrix, making it possible to work efficiently with the matrix using numerical methods. The concept of SKMs was first introduced in the late 1970s by Kannan and Chandrasekaran as an efficient way to represent and solve systems of linear equations.

Definition

A matrix A is S adjacent k-sparse when all non-zero elements in A are placed on the diagonal of the matrix. Mathematically, the matrix is represented by:

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