MATH115 Lecture Notes - Lecture 32: Matrix Addition, If And Only If, Euclidean Geometry
10 Oct 2015
School
Department
Course
Professor
Document Summary
Monday, november 17 lecture 32: abstract vectors spaces and subspaces. Expectations: define abstract vector space, define closure under an operation, distinguish between sets which are vector spaces and those that are not, prove: if in and v in v are such that v = 0. Then either = 0 or v = 0. course this set is the real numbers ) whose elements will be denoted by , , , 32. 1 definitions an abstract vector space, (v , +, scalar multiplication), is: a set v whose elements v are called vectors. With this set v is a set of scalars (in this: on this set v are defined two operations : Addition + : scalar multiplication: u + v : w in v, 32. 2 proposition : let v be a vector space. Then: 0v = 0, for all v in v, 0 = 0 for all in , ( 1)v = v, for all v in v.
