Adjoint

Affine

All Bases have same size

Bijective

Cauchy-Schwarz Inequality

Closure (Algebra)

Complement of Subspace Generates Direct Sum

Complementary Subspaces

Composition

Composition Rules for Matrices

Conditions for Diagonalizability

Criterion for a Basis

Criterion for Direct Sum

Criterion for Invertibility using Upper Triangular

Criterion for Subspace

Criterion for Upper Triangular Matrix

Dependence Lemma

Determinants for Linearly Transformed Autocorrelation Matrices

Diagonal

Diagonalizable

Dimensionality & Linear Maps

Direct Sum

Distinct eigenvalues have linearly independent eigenvectors

Double Complement Returns the Original Subspace

Eigendecomposition of a Matrix

Eigenvalues are Diagonal Elements of Upper Triangular

Eigenvector

Enough Diagonal Elements Imply Diagonalizability

Every Spanning Set Contains a Basis

Existence of Eigenvalues on Complex Spaces

Existence of Upper Triangular Matrices on Complex Spaces

Finite Basis

Finite Dimensional

Finite Variance = Autocorrelation symmetric + positive semidefinite

Identity Map

Image

Injectivity, surjectivity, and isomorphism are equivalent when Dimension is the Same

Inner Product

Inner Product Space

Intersection of Sets

Invariant

Invariant Subspace

Inverse Property of Matrix of Linear Map

Inverse to a Linear Map is Unique

Invertibility

Isomorphic Vector Spaces have the Same Dimension

Isomorphism is a Bijection

Jordan Canonical Form

Kernel

Kernel and Image are Subspaces

Linear Combination

Linear Independence

Linear Independent Sets are Smaller than Spanning Sets

Linear Map

Linear Map is Injective iff Kernel is 0

Linear maps are defined on a basis

Linear Maps are Isomorphic to their Matrices

Linear Operator

Linear Transform for Autocorrelation Matrices

Linearity Properties of Matrices

Linearly Independent Sets Generate Bases

Matrix of Linear Map

Norm-Preserving Matrix

Orthogonal

Orthogonal Complement

Orthogonal Decomposition

Orthogonal Matrices have Determinant 1

Orthogonal Matrix

Orthogonal Vector

Orthonormal

Orthonormal Matrix

Parallelogram Equality

Positive Definite

Positive Definite = Positive Eigenvalues

Positive Semidefinite

Positive Semidefinite has dim Eigenvectors

Preimage

Properties of Linear Maps

Properties of Orthogonal Complements

Rank

Rank Nullity Theorem

Set of Linear Maps

Singular

Span

Span of Vectors is a Subspace of the Vector Space

Subspace

Sum of Subsets

Sum of Subspaces is a Subspace

Sum of Subspaces is Smallest Subspace Containing their Union

The Orthogonal Complement is a Complementary Subspace

Trace

Trace and Determinant with Eigenvalues

Union of Sets

Upper-Triangular

Vector Space