MATH 415 Study Guide - Final Guide: Orthonormality, Dot Product, Base Jumping

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

Document Summary

Suggested practice exercises: chapter 3. 1: 2, 5, 7, 8, 9, 10, 11, 12, 14, 15, Khan academy video: vector dot product and vector length. Strang lectures: lec 14: orthogonal vectors and subspaces. The inner product (or dot product or scalar product) of v, w rn is v w = vt w = v1w1 + + vnwn. v w is a scalar, not a vector. Let u, v and w be vectors in rn, and let c be any scalar. De nition: the norm (or length) of a vector v rn is kvk = v v = qv2. This is the distance to the origin: the distance between points v, w rn is dist (v, w) = kv wk. The distance from v to w is zero if and only if v = w. = p12 + ( 1)2 + 32 = 11. 3 (cid:13)(cid:13)(cid:13)(cid:13)(cid:13)(cid:13) (cid:13)(cid:13)(cid:13)(cid:13)(cid:13)(cid:13) dist(cid:18)(cid:20)x1 y1(cid:21) ,(cid:20)x2 y2(cid:21)(cid:19) = k(cid:20)x1 x2 y1 y2(cid:21)k = p(x1 x2)2 + (y1 y2)2.