Chapter 7 - Complex Vector Spaces and General Inner Products

Abstract

In Section 7.1, we study Cn, the set of complex n-vectors, and consider its similarities to and differences from Rn. In Section 7.2, we examine properties of the eigenspaces of matrices with complex entries. Section 7.3 compares the properties of general complex vector spaces and linear transformations with their real counterparts. In Section 7.4, we study the complex analogs of the Gram-Schmidt Process and orthogonal matrices. Finally, in Section 7.5, we discuss inner product spaces, which possess an additional operation analogous to the dot product on Rn.