MATH 415 Final: Math415_Fa2018_Lecture24.Article

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

Document Summary

Suggested practice exercises: ch 3. 1: 7, 8, 9, 10, 11, 12, 14, 15, 17, 18, 19, Khan academy videos: introduction to orthonormal bases, coordinates with respect to orthonormal bases. Strang lectures: lec 18: change of basis, image compression / lec 14: or- thogonal vectors and subspaces. 1. 1: v, w rn are orthogonal i v w = vt w = v1w1 + vnwn = 0. This means they are perpendicular, or one of them is zero. An orthogonal basis for rn is a set {x1, x2, . , xn} so that xi xj = 0 for i 6= j (and all xi not the zero vector). An orthonormal basis for rn is a set {u1, u2, . 0 for i 6= j and ui ui = 1. , un) be an orthonormal basis for rn, and let x be some vector in rn.