MATB24H3 Lecture Notes - Diagonal Matrix, Diagonalizable Matrix, Linear Map
Document Summary
Suppose that t : v v is a linear transformation from vector space. V with ordered basis b into the vector space v with ordered basis b . [t ]b, b be the matrix representation of t relative to b amd b . T : v w be a linear transformation from the vector space v to the vector space w with ordered basis b . Then [t t ]b,b = [t ]b , b [t ]b, b . This follows from the fact that for all v v and v v we have that: (t (v))b = [t ]b,b vb, (t (v ))b = [t ]b ,b v . B : let v = t (v, (cid:0)(t t )(v)(cid:1)b = (t (t (v)))b = [t ]b b (t (v))b = [t ]b ,b [t ]b,b vb. Now suppose that b and b are two ordered bases of v and t : v v is a linear transformation.
