# Linear Algebra, Infinite Dimensions,

and Maple

### Preface
for these notes.

###

### 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

###

### Index for
these notes.

###

### Maple Constructions for the Text

###