Eigenvalues and Eigenvectors of Boolean Matrices with Application to Attractor Analysis of Boolean Networks

This article explores the eigenvalues and eigenvectors of Boolean matrices, and applies them to the attractor analysis of Boolean networks (BN s). The eigenvalues and eigenvectors of Boolean matrices over the Galois field are firstly defined. Then, the characteristic polynomial, similarity, diagonalization and generalized eigenvectors of Boolean matrices are discussed. Finally, the eigenvalues and eigenvectors of Boolean matrices are applied to analyze the attractors of a given BN.