This appendix contains important ideas about complex numbers, sets, and the logic and techniques of forming proofs. It is not meant to be read straight through, but you should head here when you need to review these ideas.

We choose to expand the set of scalars from the real numbers, {ℝ}^{}, to the set of complex numbers, {ℂ}^{}. So basic operations with complex numbers (like addition and division) will be necessary. This can be safely postponed until your arrival in Section O, and a refresher before Chapter E would be a good idea as well.

Sets are extremely important in all of mathematics, but maybe you have not had much exposure to the basic operations. Check out Section SET. The text will send you here frequently as well. Visit often.

This book is as much about doing mathematics as it is about linear algebra. The “Proof Techniques” are vignettes about logic, types of theorems, structure of proofs, or just plain old-fashioned advice about how to do advanced mathematics. The text will frequently point to one of these techniques in advance of their first use, and for specific instructions there will be additional references. If you find constructing proofs difficult (we all did once), then head back here and browse through the advice for second or third readings.

Section CNO Complex Number Operations

Subsection CNA: Arithmetic with complex numbers

Subsection CCN: Conjugates of Complex Numbers

Subsection MCN: Modulus of a Complex Number

Section SET Sets

Subsection SC: Set Cardinality

Subsection SO: Set Operations

Section PT Proof Techniques

Proof Technique D: Definitions

Proof Technique T: Theorems

Proof Technique L: Language

Proof Technique GS: Getting Started

Proof Technique C: Constructive Proofs

Proof Technique E: Equivalences

Proof Technique N: Negation

Proof Technique CP: Contrapositives

Proof Technique CV: Converses

Proof Technique CD: Contradiction

Proof Technique U: Uniqueness

Proof Technique ME: Multiple Equivalences

Proof Technique PI: Proving Identities

Proof Technique DC: Decompositions

Proof Technique I: Induction

Proof Technique P: Practice

Proof Technique LC: Lemmas and Corollaries

Subsection CNA: Arithmetic with complex numbers

Subsection CCN: Conjugates of Complex Numbers

Subsection MCN: Modulus of a Complex Number

Section SET Sets

Subsection SC: Set Cardinality

Subsection SO: Set Operations

Section PT Proof Techniques

Proof Technique D: Definitions

Proof Technique T: Theorems

Proof Technique L: Language

Proof Technique GS: Getting Started

Proof Technique C: Constructive Proofs

Proof Technique E: Equivalences

Proof Technique N: Negation

Proof Technique CP: Contrapositives

Proof Technique CV: Converses

Proof Technique CD: Contradiction

Proof Technique U: Uniqueness

Proof Technique ME: Multiple Equivalences

Proof Technique PI: Proving Identities

Proof Technique DC: Decompositions

Proof Technique I: Induction

Proof Technique P: Practice

Proof Technique LC: Lemmas and Corollaries