MATH136 Lecture Notes - Ais People, Linear Combination, Solution Set

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

Document Summary

Wednesday, march 5 lecture 23 : coordinates of a vector with respect to a basis. 23. 2 definition if v is a vector in the vector space v which has an ordered basis. Then the unique coefficients 1, 2, , k used to express v as a linear combination of. B = {v1, v2, , vk} are called the coordinates of v with respect to the basis b. We will represent these k unique scalars 1, 2, , k by [v]b , i. e. , Since is expressed as a k-tuple, the order of i"s must respect the order in which the elements of the basis b ={v1, v2, , vk } are given. We refer to b as an ordered basis. Since ( 1, 7) = 1e1 + 7e2, then the unique coordinates [v]s of v with respect to the basis s are: suppose s = {e1, e2} is the standard basis of v = 2.