Partitioned Matrices

Abstract

This chapter is devoted to the techniques of partitioned (block) matrices. Topics include elementary operations, determinants, and inverses of partitioned matrices. We begin with the elementary operations of block matrices, followed by discussions of the inverse and rank of the sum and product of matrices. We then present four different proofs of the theorem that the products AB and BA of matrices A and B of sizes m × n and n × m, respectively, have the same nonzero eigenvalues. At the end of this chapter we discuss the often-used matrix technique of continuity argument.