MATH 204 Lecture Notes - Lecture 8: Empty Set, Scalar Multiplication, Vector Space
6 Nov 2017
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Step 3 (i) an operation denoted as: + (ii) an operation denoted as: * Step 1 consider s as a non empty set of elements. * operates on one object in s and a scalar (scalar is not necessarily in s ) Step 3 the following 10 property structures (axioms) must apply for the two operations: = u: for each u there is an element in s such that: If the scalars are contained in the real numbers then s is called a. Is r(cid:2924) with its regular addition and scalar multiplication a vector space : r(cid:2870) (i) denotes rxr and is called a. An ordered pair (a, b), both a and b contained in r (real numbers) An ordered n-tuple (a(cid:2869), a(cid:2870), , a(cid:2924)) where a(cid:2919) are real numbers. * is defined as regular scalar mult. a(cid:2869)a(cid:2870). a(cid:2924) b(cid:2869)b(cid:2870). b(cid:2924)
