MATA23H3 Lecture Notes - Lecture 15: Linear Map, Row And Column Spaces, Scalar Multiplication
Document Summary
Mata23 - lecture 15 - properties of linear transformations continued. Kernel, range, rank, and nullity: let t : rn rm be a linear transformation and a be the standard matrix representations of. T , such that t ((cid:126)x) = a(cid:126)x. Kernel of t : ker(t ) = (cid:126)x rn|a(cid:126)x = (cid:126)0 (cid:110) (cid:111) (cid:126)x rn|t ((cid:126)x) = (cid:126)0. = the null space of a (cid:111) rn. Range of t : range(t ) = {t ((cid:126)x) rm|(cid:126)x = rn} rn. = {a(cid:126)x|(cid:126)x rn} = the column space of a. Rank of t : rank(t ) = the dimension of the range of t. = the dimension of the column space of a. Nullity of t : nullity(t ) = the dimension of the kernel of t. = the dimension of the null space of a = nullity(a: let t : rn rm be a linear transformation.
