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Engineering Entrance > Learn Mathematics for Engineering Entrance for Beginners to Advanced > What is vector space ?
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What is vector space ?

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BE & MBA having more than 10 years of teaching experience

A vector space consists of a set of vectors and a set of scalars that is closed under vector addition and scalar multiplication. That is, when you multiply any two vectors in a vector space by scalars and add them, the resulting vector is still in the vector space.
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Avector spaceconsists of a set of vectors and a set of scalars that is closed under vector addition and scalar multiplication. That is, when you multiply any two vectors in a vector space by scalars and add them, the resulting vector is still in the vector space. read less
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Home Tutor with experience of 13 Years in field of specifically Science and Physics

It is a set of vector Which includes arithmetic calculation like adding and forming a new vector. Same goes for scalar multiplication also..... Suppose x y z are vector and (x y z ) ∈ V V is set of vectors
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PhD chemistry, Students friendly guidance

A vector space is a set of elements called vectors, which can be added together and multiplied by numbers called scalars, following specific rules (axioms). These operations are defined to be closed, meaning adding two vectors or multiplying a vector by a scalar results in another vector within the same...
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A vector space is a set of elements called vectors, which can be added together and multiplied by numbers called scalars, following specific rules (axioms). These operations are defined to be closed, meaning adding two vectors or multiplying a vector by a scalar results in another vector within the same space. read less
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IIT GATE-qualified Math Educator | 10+ yrs exp | JEE, 11–12th, Engg Maths, CAT, GRE, GMAT, IB/IGCSE

A very simple definition: It’s a collection of vectors where addition and scaling work normally and follow basic mathematical rules.
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A vector space is a collection of objects that can be added and scaled, and still stay in the collection, following some simple rules. A set V is a vector space over a field F (usually real numbers ℝ) if: 1. You can add elements of V. 2. You can multiply elements of V by scalars from F. 3....
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A vector space is a collection of objects that can be added and scaled, and still stay in the collection, following some simple rules. A set V is a vector space over a field F (usually real numbers ℝ) if: 1. You can add elements of V. 2. You can multiply elements of V by scalars from F. 3. The result always stays inside V. 4. The operations satisfy 8 basic axioms (r ules). read less
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Kannada Assistant professor with 6 Years of Teaching Experience

A Gentle Introduction to Vector Space Models ...A vector space is a set of elements called vectors, which can be added together and multiplied by numbers called scalars, following specific rules (axioms). These operations are defined to be closed, meaning adding two vectors or multiplying a vector by...
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A Gentle Introduction to Vector Space Models ...A vector space is a set of elements called vectors, which can be added together and multiplied by numbers called scalars, following specific rules (axioms). These operations are defined to be closed, meaning adding two vectors or multiplying a vector by a scalar results in another vector within the same space. read less
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