transition matrices

Summary

Algorithm to find transition matrix

• extension of the algorithm for computing coordinates

Inverse of transition matrix

inverse is defined when the transition preserves dimension

Concept

Transition matrix

• coordinates of the vectors in relative to the basis

intuition: any matrix is a standard basis to its column space

Linear independence of relative coordinates

(1) applies to the negation as well, ie. if the set was linearly dependent

Number of basis vectors

Application

Transition matrix from the standard basis

the matrix of the vectors in , is a transformation from the standard basis to the basis