VECTOR SPACE Meaning and
Definition
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A vector space is a fundamental concept in linear algebra, providing a structure to study and manipulate vectors and their properties. It is a mathematical framework consisting of a set of objects called vectors, along with two operations: vector addition and scalar multiplication. These operations must satisfy specific conditions to define the vector space.
In a vector space, vectors can be added together using vector addition, which follows the parallelogram law. This means that if two vectors are added, the resulting vector is determined by the parallelogram formed by the original vectors. Scalar multiplication allows us to scale vectors by multiplying them by a scalar quantity, such as a real number, producing a new vector.
To qualify as a vector space, certain conditions must be met. The vector addition operation should be commutative and associative, meaning the order of addition and grouping doesn't change the result. There must also be an additive identity, where adding it to any vector yields that same vector. Additionally, each vector should have an additive inverse, such that adding a vector and its inverse gives the additive identity.
The concept of a vector space is extremely versatile and applicable to various fields of mathematics, physics, and computer science. It provides a rigorous framework for studying vectors and their properties, enabling us to analyze and solve problems involving linear equations, transformations, and many other mathematical structures.
Common Misspellings for VECTOR SPACE
- cector space
- bector space
- gector space
- fector space
- vwctor space
- vsctor space
- vdctor space
- vrctor space
- v4ctor space
- v3ctor space
- vextor space
- vevtor space
- veftor space
- vedtor space
- vecror space
- vecfor space
- vecgor space
- vecyor space
- vec6or space
- vec5or space
Etymology of VECTOR SPACE
The word "vector" is derived from the Latin term "vehere", which means "to carry". It was first introduced in mathematics in the mid-18th century to represent a quantity possessing both magnitude and direction, similar to a geometric line segment.
The term "space" refers to a mathematical structure that consists of a set of elements. In the context of vector spaces, it represents the set of vectors.
The concept of a vector space was developed in the late 19th and early 20th centuries by mathematicians such as Giuseppe Peano, David Hilbert, and Hermann Grassmann. The term "vector space" was coined as an English translation of the German phrase "Vektorraum", which was introduced by Grassmann in his influential work on geometric algebra. The term has been widely adopted in English-speaking mathematical literature since then.
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