MATH136 Lecture Notes - Lecture 19: Spain, Matrix Addition, Scalar Multiplication

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Sproule

Document Summary

Monday, february 24 lecture 19: abstract vectors spaces and subspaces. Concepts: abstract vector space, closure under an operation, prove: if in and v in v are such that v = 0. Then either = 0 or v = 0: recognize n, the set of all m by n matrices, mn,m, and all functions f on [0,1] as examples of vector spaces. 19. 1 definition let v be a set on which we have define addition + and scalar multiplication. There exists in v an element 0 such that v + 0 = v for all v in v. (additive with 0 axiom) For all v in v. there exists in v an element v such that v + v = 0. (additive inverse axiom: scalar properties, the elements in v distribute over finite sums of scalars. Scalars distribute over finite sums of elements of v. ( )v = ( v)