Basis Vectors - Types

Standard Basis Vectors	is a basis whose vectors are composed of all zeroes, except one that equals 1 is also a type of orthogonal basis
Eigenbasis Eigenvector Basis	is a basis for a vector space consisting entirely of eigenvectors
Orthogonal Basis Vectors	is a basis whose vectors are mutually orthogonal
Orthonormal Basis Vectors	is a basis whose vectors are mutually orthonormal is an orthogonal basis whose vectors are of unit length
Dual Basis	Click here to expand... is a set of vectors that spans a finite-dimensional algebraic dual space given a vector space 𝑉 with a basis 𝐵 of vectors indexed by an index set 𝐼 (the cardinality of 𝐼 is the dimension of 𝑉), the dual set of 𝐵 is a set 𝐵 $$ of vectors in the dual space 𝑉 with the same index set 𝐼 such that 𝐵 and 𝐵* form a biorthogonal system. The dual set is always linearly independent but does not necessarily span 𝑉. If it does span 𝑉, then 𝐵* is called the dual basis or reciprocal basis for the basis 𝐵. is a (1,0)-tensor

Basis Vectors - Linear Transformation Intuition