basis vectors


Summary

Standard basis

Equivalent statements of invertibility

idea of row and column space is relevant here

Algorithm for computing relative coordinate

note: this is a transition from the standard basis

Concept

Basis

every vector in can be expressed as a linear combination of the basis vectors

Relative coordinates

  • the coordinates wrt. another basis
  • unique linear combination of the basis vectors that maps to a vector in the standard basis

Unique relative coordinate

Application

Extra