MATH 204 Study Guide - Final Guide: Henri Poincaré, Scalar Multiplication, Zero Element

• School: Concordia University
• Department: Mathematics
• Course: MATH 204
• Professor: Magloire LOUDEGUI DJIMDOU

Document Summary

Mathematics is the art of giving the same name to di erent things. Let v be an arbitrary nonempty set of objects (real numbers, vectors, functions, matrices), on which two operations are de ned: addition and scalar multiplication. Consider the space which only element is the zero vector: v = {0}. And de ne 0 + 0 = 0 (addition) and k0 = 0 (scalar multiplication). We check the axioms: 0 + 0 = 0, 0 + 0 = 0 + 0, 0 + (0 + 0) = ( 0 + 0) + 0: let u v (that is u = 0). Then: u + 0 = 0 + 0 = 0 + u = 0: for u v (that is u = 0), let u = 0. Then: u + ( u) = 0 + 0 = ( u) + u = 0: let u v (that is u = 0) and k be a scalar.