Mathematical Calculation of Inclusion Domain Complex Matrix of Block Eigenvalues Under Two Part

Abstract

AbstractUnder the two parts of the set, find the inclusion domain of the block eigenvalues of the block composite matrix. In the block matrix, it is mainly used to simplify the operation when the matrix order is higher. For the block in the block matrix the compound matrix means that the sub-blocks can be exchanged with each other. On this basis, the inclusion domain of the block eigenvalues is studied. Based on this, this paper launches the mathematical calculation research of the complex matrix of the block eigenvalue inclusion domain under the two parts. This paper adopts the basic theory of linear algebra, matrix inequality theory, convex function basic theory, probability theory, linear matrix inequality theory, and algebraic inequalities in the real number domain. This paper uses the convex function properties to improve the distribution of the eigenvalues of general complex matrices, obtains the corresponding localization area, and uses specific numerical examples to verify the validity of our results. In addition, based on the above conclusions, this paper further obtains the estimation formulas for the upper and lower bounds of the matrix expansion, which is used for eigenvalue estimation and positioning problems, and obtains the estimation formulas for the best matching distance of any two complex matrices. This paper uses numerical algebraic inequalities to study the location and estimation of polynomial roots, gives a series of corresponding estimation regions of characteristic roots, and verifies the validity of the conclusions through specific numerical examples. The research results show that the structure similarity SSIM value obtained by the algorithm in this paper is larger and closer to 1 than the SSIM value obtained by other algorithms, which is in line with people’s visual senses.KeywordsTwo-part underlineBlock coincidence matrixBlock eigenvalueInclusion domain