Course Material

We will mainly follow the book

Metrics, Norms, Inner Products and Operator Theory, by C. Heil (2018).

This book is available free of charge if you access the Springer web page via the NTNU network (use vpn client). Whenever needed, and certainly towards the end of the course, the book will be supplemented by lecture notes. These will be posted online.

• Chapter 1
• Chapter 2: 2.1–2.6, 2.8–2.9
• Chapter 3
• Chapter 4: 4.1–4.2, 4.4–4.5 and Theorem 4.6.2 in chapter 4.6
• Chapter 5: 5.1–5.9, 5.11
• Chapter 6: 6.1–6.6, 6.8

• Note on Banach's Fixed Point Theorem
• Note on adjoint operators
• Note on selected topics in linear algebra

You might also find the following books useful and/or interesting:

• Friedberg et. al: Linear Algebra, 4th ed, Pearson.
• Kreyszig: Introductory Functional Analysis with Applications, John Wiley & Sons.
• Steele: The Cauchy-Schwarz Master Class, Cambridge Univ. Press.
• Strang: Linear algebra and its applications, 4th ed, Brooks/Cole.
• Young: An introduction to Hilbert space, Cambridge Univ. Press.