Linear Algebra, Infinite Dimensions, and Maple can be downloaded free of charge in pdf format. These notes evolved in the process of teaching a beginning graduate course in Hilbert Spaces.

## Book Description

The first edition was simply personal, handwritten notes prepared for lecture. A copy was typed and given to the students, for it seemed appropriate that they should have a statement of theorems, examples, and assignments. With each teaching of the course, the notes grew.

## Table of Contents

- A Decomposition for Matrices
- Exp(tA)
- Self Adjoint Transformations in Inner-Product Spaces
- The Gerschgorin Circle Theorem
- Convergence
- Orthogonality and Closest Point Projection
- Orthogonal, Nonexpansive, & Self-Adjoint Projections
- Orthonormal Vectors
- The Finite Dimensional Paradigm
- Bounded Linear Maps from E to C
- Applications to Differential Equations
- The Simple Paradigm from E to E
- Adjoint Operators
- Compact Sets
- Compact Operators
- The Space of Bounded Linear Operators
- The Eigenvalue Problem
- Normal Operators and The More General Paradigm
- Compact Operators and Orthonormal Families
- A Characterization of Compact Operators
- The Fredholm Alternative Theorems
- Closed Operators
- The Deficiency of A
- A Problem in Control
- Approximation in a Hilbert Space with a reproducing kernel