Linear Algebra

Core idea

Click any term to expand its definition inline.

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Vector Spaces

• Vector space
• Euclidean space

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Linear Maps

• Linear map
• Linear operator

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Eigentheory

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

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Matrix Invariants

• Determinant
• Positive semidefinite matrix
• Trace

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Inner Products and Norms

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

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Function Spaces

• Banach space
• Hilbert space
• Compact operator

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Theorems

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

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Conjecture dependencies

• Unit sphere of a normed space
• Surjective linear isometry
• Orthonormal basis
• Closed linear subspace
• Orthogonal complement
• Orthogonal projection
• Invariant subspace of an operator

Quaternionic and Hermitian linear algebra

• Complexification
• Quaternion division algebra
• Quaternionic vector space