Elementary Concepts of Vector Spaces and Modules
Explore elementary concepts of vector spaces and modules, including definitions, properties, and operations. Presented by Mrs. M. L. Dhumal, Assistant Professor & Head, Department of Mathematics, Deogiri College, Aurangabad.
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Topic VECTOR SPACES AND MODULES Presented by Mrs. M. L. Dhumal Assistant Professor & Head Department of Mathematics Deogiri College, Aurangabad
CHAPTER 1: VECTOR SPACES AND MODULES Elementary basic concepts, Linear independence and bases, Dual spaces, Inner product spaces, Modules
ELEMENTARY BASIC CONCEPT VECTOR SPACE DEFINITION: A non-empty set V is said to be a vector space over a field F if V is an abelian group under an operation which we denote by + and if for every there is defined an element, written as v in V subject to F, v V 1. (v + w) = av + aw; 2. ( + )v = v + v; 3. ( v) = ( )v; 4. 1v = v; for all , F, v, w V (where the 1 represents the unit element of F under multiplication).
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