Sufficient Conditions Analysis of Coverage Algorithm Constructed Positive Definite Tridiagonal Matrices in WSNs

Sufficient Conditions Analysis of Coverage Algorithm Constructed Positive Definite Tridiagonal Matrices in WSNs

In this paper, we have studied the coverage algorithm constructed positive definite Tridiagonal Matrices for identifying the positive definite symmetric matrix together with the properties in Wireless sensor networks (WSNs). Firstly, we have summarized the determinations of the positive definite symmetric matrix, respectively, from four different aspects including the definition, the Jordan normal form, the upper-left sub-matrices and the decomposition of the positive definite matrix. At the same time, the objects and precautions applying to the different positive definite matrices are described in detail. Secondly, we study the relevant properties of positive definite matrix, and construct the positive definite matrix by using the non-degenerate matrix on the basis of the determination of positive definite symmetric matrix. Finally, we prove the inequality of Hadamard in solving the practical problems by using the positive definite matrix. Furthermore, we get the Cauchy-Schwarz inequality satisfied with positive definite matrix [1-16].