NAVIGATION

Home

Research

Bookshelf

Garden

FIND ME ON

GitHub

LinkedIn

Home

Research

Bookshelf

Garden

Finite Basis

šŸŒ±

Definition
LinearAlgebra

A (finite) basis of a vector space is a (finite) set of linearly independent vectors {v1,...,vk}\{v_1,...,v_k\} such that V=span(v1,...,vk)V=span(v_1,...,v_k).

Linked from

Diagonalizable

Matrix of Linear Map

Finite Basis

Finite Dimensional

Linear Independence

Linear maps are defined on a basis

Conditions for Diagonalizability

Enough Diagonal Elements Imply Diagonalizability

Composition Rules for Matrices

Linearity Properties of Matrices

Criterion for Invertibility using Upper Triangular

Criterion for Upper Triangular Matrix

Eigenvalues are Diagonal Elements of Upper Triangular

Existence of Upper Triangular Matrices on Complex Spaces

All Bases have same size

Criterion for a Basis

Every Spanning Set Contains a Basis

Linearly Independent Sets Generate Bases

Lattice

Second-countable