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In linear algebra, a vector space is a mathematical structure consisting of a set of vectors along with operations of vector addition and scalar multiplication. These operations must satisfy certain properties, including closure under addition and scalar multiplication, associativity, commutativity of...

read more In linear algebra, a vector space is a mathematical structure consisting of a set of vectors along with operations of vector addition and scalar multiplication. These operations must satisfy certain properties, including closure under addition and scalar multiplication, associativity, commutativity of addition, existence of an additive identity (zero vector), existence of additive inverses, and compatibility of scalar multiplication with field multiplication.In simpler terms, a vector space is a collection of vectors that can be added together and multiplied by scalars, meeting specific algebraic rules. It serves as a fundamental concept in linear algebra and provides a framework for studying linear transformations and systems of linear equations.

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Vector Space. A vector space is a nonempty set V of objects, called vectors, on which are defined two operations, called addition and multiplication by scalars (real numbers), subject to the ten axioms below. The axioms must hold for all u, v and w in V and for all scalars c and d.

read more Vector Space. A vector space is **a nonempty set V of objects, called vectors, on which are defined two operations, called addition and multiplication by scalars (real numbers)**, subject to the ten axioms below. The axioms must hold for all u, v and w in V and for all scalars c and d.

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Vector Space. A vector space is a nonempty set V of objects, called vectors, on which are defined two operations, called addition and multiplication by scalars (real numbers), subject to the ten axioms below. The axioms must hold for all u, v and w in V and for all scalars c and d.

read more Vector Space. A vector space is **a nonempty set V of objects, called vectors, on which are defined two operations, called addition and multiplication by scalars (real numbers)**, subject to the ten axioms below. The axioms must hold for all u, v and w in V and for all scalars c and d.

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