Finite Dimensional

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Definition

LinearAlgebra

Definition (Finite Dimensional)

A Vector Space $V$ is called finite dimensional if $V=0$ or $V$ has a basis $\{v_1,...,v_n\}$ . The dimension of $V$ is the number of elements in a basis, and is written $dim(V)=n$ If $V=0$ , then $dim(V)=0$ .

Linked from

Continuous-time Gaussian process motion planning via probabilistic inference

Invertibility

Diagonalizable

Matrix of Linear Map

Rank

Existence of Eigenvalues on Complex Spaces

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

Rank Nullity Theorem

Conditions for Diagonalizability

Enough Diagonal Elements Imply Diagonalizability

Linear Maps are Isomorphic to their Matrices

Linearity Properties of Matrices

Criterion for Invertibility using Upper Triangular

Criterion for Upper Triangular Matrix

Eigenvalues are Diagonal Elements of Upper Triangular

Linearly Independent Sets Generate Bases

Complement of Subspace Generates Direct Sum

Double Complement Returns the Original Subspace

The Orthogonal Complement is a Complementary Subspace

Isomorphic Vector Spaces have the Same Dimension

Four Hypotheses

Stationary Conditions for Team Optimality

Radner Krainak Theorem

Characteristic of F

Min poly. dividing poly. of same root

Same Finite-Dimensional Distribution