MATH 105L Lecture Notes - Lecture 5: Linear Map, Scalar Multiplication, Row And Column Vectors
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8/1/2010 1:59:00 am: linear transformation operations, (t+s)(v)=t(v) + s(v, (ct)(v)= ct(v, theorem 5. 6, if t: v w and s: v w are linear transformations, then so are. 8/1/2010 1:59:00 am: matrix of t with respect to bases and , [t] . = = a11 a1n a21 a2n am1 amn: theorem 5. 10, suppose t: v w and s: w u are linear transformations. If is a basis for v, is a basis for w, and is a basis for. P: corollary 5. 13, if t: v v, [t] . P: theorem 5. 14, suppose t: v w is a linear transformation. Let be a basis for v and be a basis for w. if v is a vector in v, [v] where [v] is the coordinate vector of v: corollary 5. 15, if t: rn rm is a linear transformation and a the matrix t with respect to the standard basis for rn and rm, then.
