Program Design and Implementation of Y Class Matrix Eigenvalue Based on Python Language

Abstract

Matrix eigenvalues have important applications in rice yield, collaborative filtering recommendation algorithm integrating user interests and score differences, so solving matrix eigenvalue algorithm is one of the research hotspots in the algorithm field. Dichotomy is a very important algorithm for solving matrix eigenvalues. Based on the study of solving matrix eigenvalue algorithm by experts and scholars $\mathbf{Y}$ class matrix is studied. The matrix has seven pairs of adjacent two paramagnetic submatrixes, and the eigenvalues are not strictly interleaved, that is, the matrix does not meet the key properties of using dichotomy to solve the eigenvalues. By studying and analyzing the principle of sign change of characteristic polynomial sequence of sequential principal submatrix of $\mathbf{Y}$ class matrix, the feasible conditions and feasibility of dichotomy algorithm for solving the eigenvalues of Y-type matrix are studied. The numerical experiment uses Python language to design the program to verify the feasibility of the algorithm.