Section 19.2 Terminology and notation
- basis for a vector space
a linearly independent spanning set
- ordered basis
a basis where the basis vectors are always written in a particular order, and linear combinations of the basis vectors are always expressed in that order
- coordinates of a vector w relative to a basis B={v1,v2,…,vn}
the unique set of scalars c1,c2,…,cn so that w=c1v1+c2v2+⋯+cnvn
- coordinate vector associated to a vector w relative to a basis B
the vector (c1,c2,…,cn) in Rn formed by the coordinates of w relative to B
- (w)B
notation to mean the coordinate vector (c1,c2,…,cn) in Rn for the vector w, relative to the basis B for the vector space that contains w
- [w]B
notation to mean the coordinate vector in Rn for the vector w, relative to the basis B for the vector space that contains w, realized as a column vector (i.e. as a column matrix)