Applied Mathematics 1411A/B Lecture Notes - Lecture 8: Pythagorean Theorem, Orthogonality, Nspace

• School: Western University
• Department: Applied Mathematics
• Course: Applied Mathematics 1411A/B
• Professor: Natalia Kiriushcheva

Document Summary

Norm, dot product, and distance in rn (3. 2; pg. Definition: we define the euclidean norm (or euclidean length) of a vector. Theorem (properties of length in scalar, then: nr ): if u and v are vectors in nr , and k is any. Definition: the vector u is a unit vector if. ____) is a unit vector. nr are the vectors with one component equal. 1 vv d nv vu nr is defined by in vu u. ,( vud nr ): if u, v, and w are vectors in nr , and k is any. Definition: if the dot product (also called the euclidean inner product) uu vv and. 22 are any two vectors in is defined by nr , then vu nnvu. Note: it is common to refer to and the euclidean inner product as euclidean n-space. nr with the operations of addition, scalar multiplication,