MATH 4389 Study Guide - Final Guide: Row Echelon Form, Scalar Multiplication, Row And Column Spaces

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19 Apr 2017
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Brie y, a vector space consists of a set of objects called vectors along with a set of objects called scalars. The vector space axioms concern the algebraic relationships among the vectors and scalars. They may be found in any of the above references. Vectors can be added to form new vectors. Vectors can also be multiplied by scalars to form new vectors. There is one vector, called the zero vector, that acts as an identity element with respect to addition of vectors. Each vector has a negative associated with it. The sum of a vector and its negative is the zero vector. In summary, the set of vectors with the operation of vector addition is an abelian group. The set of scalars is an algebraic eld, such as the eld of real numbers or the eld of complex numbers. Multiplication of scalars by vectors distributes over addition of vectors and also over addition of scalars.