MATH 4377 Lecture Notes - Lecture 1: Associative Property, Additive Inverse, Even And Odd Functions
Document Summary
1. 1 introduction: vectors in (real) 2 dimensional and. Example: give a parametric representation of the line through (cid:4666)(cid:884),(cid:885),(cid:3398)(cid:884)(cid:4667) and (cid:4666)(cid:3398)(cid:886),(cid:884),(cid:883)(cid:4667). Example: give a parametric representation of the plane that passes through (cid:4666)(cid:883),(cid:3398)(cid:884),(cid:885)(cid:4667), (cid:4666)(cid:883),(cid:886),(cid:884)(cid:4667) and (cid:4666)(cid:885),(cid:884),(cid:882)(cid:4667). Vecto or rules in (cid:2174)(cid:2779) a and (cid:2174)(cid:2780): (the m motivatio on for m more genneral things to ccome )) We st tart with h the no tion of a a field. The ele ments in n a field and (cid:2174)(cid:2780) Gener ralizatio on of ve ector pro operties s: are calleed vectors. The ele ments in n a vecto or space. Examples of sets that are not vector spaces: (cid:1847)(cid:3404)(cid:4668)(cid:4666)(cid:1876),(cid:1877)(cid:4667)| (cid:1876)(cid:3397)(cid:1877)(cid:3404)(cid:883)(cid:4669) over (cid:1844) with the usual definition of vector addition and scalar multiplication. (cid:1848)(cid:3404)(cid:4668)(cid:4666)(cid:1876),(cid:1877)(cid:4667)| (cid:1876)(cid:3404)(cid:882) or (cid:1877)(cid:3404)(cid:882)(cid:4669) over (cid:1844) with the usual definition of vector addition and scalar multiplication. (cid:1849)(cid:3404)(cid:4668)(cid:4666)(cid:1876),(cid:1877)(cid:4667)| (cid:1876),(cid:1877)(cid:3410)(cid:882)(cid:4669) over (cid:1844) with the usual definition of vector addition and scalar multiplication.
