Chapter 33
Similarity of Families of Matrices
Shmuel Friedland
University of Illinois at Chicago
This chapter uses the notations, definitions, and facts given in Chapter 32. The aim of this chapter is to acquaint the reader with two difficult problems in matrix theory:
- Similarity of matrices over integral domains, which are not fields.
- Simultaneous similarity of tuples of matrices over ℂ.
Problem 1 is notoriously difficult. We show that for the local ring H0 this problem reduces to Problem 2 for certain kind of matrices. We then discuss certain special cases of Problem 2 as simultaneous similarity of tuples of matrices to upper triangular and diagonal matrices. The L-property of pairs of matrices, which is discussed next, is closely related ...
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