MATH136 Lecture Notes - Linear Combination, 2Wo

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Sproule

Document Summary

Friday, march 7 lecture 24 : change of coordinates matrix . Concepts: computing the matrix which transforms the coordinates of a vector with respect to a basis to coordinates of the same vector with respect to another basis. The matrices cpb and bpc are as follows. So cpb = [ [b1]c [b2]c [b3]c [bm]c ] maps [x]b to [x]c. Similarly, bpc = [ [c1]b [c2]b [c3]b [cm]b ] maps [x]c to [x]b. Remark note that cpb = [ [b1]c [b2]c [b3]c [bm]c ] is a generalization of the matrix. 24. 2 example suppose we are given two bases b = {b1, b2} and c = {c1, c2} for an abstract vector space v. suppose that. Suppose x is some vector in v such that x = 3b1 + b2. We modify the question : suppose, on the other hand, that [x]c = (6, 4) is known. That is, suppose we know that x = 6c1 + 4c2.