Shared Linear Algebra

This section contains definitions and theorems from linear algebra that are used throughout analysis and algebra.

Contents

Vector Spaces

• Vector space
• Euclidean space

Linear Maps

• Linear map
• Linear operator

Eigentheory

• Eigenvalue
• Eigenvector
• Eigenspace

Matrix Invariants

• Determinant
• Trace
• Characteristic polynomial
• Minimal polynomial

Inner Products and Norms

• Inner product
• Euclidean norm
• Orthogonality
• Operator norm

Theorems

• Cayley-Hamilton theorem
• Rank-nullity theorem
• Existence of a basis