MATH 415 Final: Math415_Fa2018_Lecture15.Article

• School: University of Illinois
• Department: Mathematics
• Course: MATH 415
• Professor: J Li

Document Summary

Suggested practice exercises: chapter 2. 6: 5, 6, 7, 36, 37. Khan academy videos: linear transformations / linear transformations as. Matrix vector products / linear transformation examples: rotations in. What is the point of having a basis for a vector space v : dimension! If you have a basis b = (v1, v2, . , vp) for v , you know that the dimension of v is p, so that you have an idea of the size of v . In particular, if v has dimension 0 v is just the zero vector space: coordinates! , vp) is a basis for v , we can express w in this basis. This means that we can write (uniquely!) w = x1v1 + x2v2 + + xpvp. , xp the coordinates of w with respect to the basis b. We are going to organize the coordinates in a convenient package. If w v and b = (v1, v2, .