Linear Algebra, Infinite Dimensions,
and Maple

Preface for these notes.

Chapters 1 and 2

A Decomposition for Matrices


Chapters 3 and 4

Self Adjoint Transformations in Inner-Product Spaces

The Gerschgorin Circle Theorem

Chapters 5 and 6


Orthogonality and Closest Point Projection

Chapters 7 and 8

Orthogonal, Nonexpansive, & Self-Adjoint Projections

Orthonormal Vectors

Chapters 9 and 10

The Finite Dimensional Paradigm

Bounded Linear Maps from E to C

Chapters 11 and 12

Applications to Differential Equations

The Simple Paradigm from E to E

Chapters 13 and 14 

Adjoint Operators

Compact Sets

Chapters 15 and 16

Compact Operators

The Space of Bounded Linear Operators

Chapters 17 and 18

The Eigenvalue Problem

Normal Operators and The More General Paradigm

Chapters 19 and 20

Compact Operators and Orthonormal Families

A Characterization of Compact Operators

Chapters 21 and 22

The Fredholm Alternative Theorems

Closed Operators

Chapter 23

The Deficiency of A

Chapter 24

A Problem in Control

Chapter 25

Approximation in a Hilbert Space with a reproducing kernel

Index for these notes.

Maple Constructions for the Text

Constructions in Chapters 1 and 2.

Constructions in Chapters 3 and 4,

Constructions in Chapters 5 and 6 ,

Constructions in Chapters 7 and 8 .

Constructions in Chapters 9 and 10,

Construction in Chapter 24