Simultaneously normalizable matrices
If \(A,B\in C^{n\times n}\), and there exists a nonsingular matrix W such that both \(W^{-1}AW\) and \(W^{-1}BW\) are normal, then A and B are said to be simultaneously normalizable. In this paper the author develops a necessary and sufficient condition for two matrices A and B to be simultaneously normalizable. This condition is expressed by the properties of the modal matrices (eigenvector matrices) of A and B. In addition, an application is demonstrated in the special case of simultaneously real symmetrizable matrices including geometrical interpretations, and a numerical example is given.
scientific article; zbMATH DE number 4008573
scientific article