Linear Algebra

Click any term to expand its definition inline.

Vector Spaces

• Vector space
• Euclidean space

Linear Maps

• Linear map
• Linear operator

Eigentheory

• Eigenvalue
• Eigenvector
• Eigenspace
• Characteristic polynomial
• Minimal polynomial

Matrix Invariants

• Determinant
• Trace

Inner Products and Norms

• Inner product
• Inner product space
• Bilinear form
• Orthogonality
• Norm
• Normed vector space
• Euclidean norm
• Operator norm

Function Spaces

• Banach space
• Hilbert space
• Compact operator

Theorems

• Existence of a basis
• Rank-nullity theorem
• Cayley–Hamilton theorem
• Cauchy–Schwarz inequality