Describe briefly on group theory and also vector space?
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VECTOR SPACE =) A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms .
GROUP THEORY =) In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
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VECTOR SPACE =) A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms .
GROUP THEORY =) In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
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Group theory is the study of groups. Groups are sets equipped with an operation (like multiplication, addition, or composition) that satisfies certain basic properties. As the building blocks of abstract algebra, groups are so general and fundamental that they arise in nearly every branch of mathematics and the sciences. For example:
Symmetry groups appear in the study of combinatorics overview and algebraic number theory, as well as physics and chemistry. For example, Burnside's lemma can be used to count combinatorial objects associated with symmetry groups.
A space consisting of vectors together with associative and commutative operation of addition multiplication vectors
Symmetry groups appear in the study of combinatorics overview and algebraic number theory, as well as physics and chemistry. For example, Burnside's lemma can be used to count combinatorial objects associated with symmetry groups.
A space consisting of vectors together with associative and commutative operation of addition multiplication vectors
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