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Algebra I: A Basic Course in Abstract Algebra by Rajendra Kumar Sharma, Sudesh Kumari Shah, Asha Gauri Shankar

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Chapter 13

Vector Space

13.1 Definition and Examples

There are objects in mathematics which can be added together as well as multiplied by numbers also, like polynomials, matrices, real valued functions etc. In these systems, the operations of addition and multiplication by numbers have properties which are the same as those of ℝn as given in chapter. The elements of ℝn are called vectors and the real numbers are called scalars. For this reason, an algebraic structure which has ℝn, like properties is called a vector space. In this chapter, we define and study vector spaces. A good intuitive model for a vector space is provided by ℝ2 and ℝ3.

Definition 13.1.   (Vector space): Let V be a non-empty set and F a field. Let a binary operation + be ...

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