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A preliminary section, summarizing standard definitions and results that will be needed in the rest of the book. These include spaces of analytic functions and their operators (including Hankel and Toeplitz operators). Further, some results on spectra and the convergence of sequences of vectors and operators on Hilbert spaces are described.
Previous chapters considered the Euclidean norm, the spectral norm, and the Frobenius norm. These three norms are particularly important, but there are many other important norms for applications. This chapter discusses vector norms, matrix norms, and operator norms, and uses these norms to analyze the convergence of sequences. It revisits the Moore–Penrose pseudoinverse from a norm-minimizing perspective. It applies norms to the orthogonal Procrustes problem and its extensions.
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