What is vector space ?

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A vector space is a set of vectors that are closed under vector addition and scalar multiplication, meaning adding two vectors or multiplying a vector by a scalar results in another vector within the same set. These operations must satisfy a specific set of rules, or axioms, ensuring the structure is...
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A vector space is a set of vectors that are closed under vector addition and scalar multiplication, meaning adding two vectors or multiplying a vector by a scalar results in another vector within the same set. These operations must satisfy a specific set of rules, or axioms, ensuring the structure is well-defined and can be used for things like linear algebra. Common examples include the set of all possible dimensional real number pairs and the set of polynomials. read less
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I am a Educator with 12 years of experience in IIT /Engineering Entrance Examination

A vector space or a linear space is a fundamental concept in linear algebra. We can define it as "A vector space is a collection of vectors that can be added together and multiplied (scaled) by numbers (called scalars), and the result is still a vector in the same space.
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A vector spaceor a linear spaceis a fundamental concept in linear algebra. We can define it as "A vector space is a collection of vectors that can be added together and multiplied (scaled) by numbers (called scalars), and the result is still a vector in the same space. read less
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A fundamental concept in Mathematics
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A vector space is a set of objects called vectors where you can add any two vectors and multiply a vector by a number, and the results stay inside the same set. These two operations follow a fixed set of rules. Here’s a simple way to think about it: A vector space is a collection of elements...
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A vector space is a set of objects called vectors where you can add any two vectors and multiply a vector by a number, and the results stay inside the same set. These two operations follow a fixed set of rules. Here’s a simple way to think about it: A vector space is a collection of elements where: You can add them. You can scale them (multiply by real numbers). The rules of addition and scaling always work the same way. read less
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a teacher with (M.A economics) and 4 years of experience

a vector space is collection of objects called vector which are added together and multiplied by numbers following specific rules
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Kota Faculty with 8 year of Experience

Vector space is a set in which we can add vectors or multiply it When you are learning vector in physics it is more related with direction when you are learning in maths we have example of 2D coordinates
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A **vector space** is a set of objects called **vectors** along with two operations—**vector addition** and **scalar multiplication**—that satisfy certain rules (axioms). Formally, a set over a field (like real numbers ℝ) is a vector space if: 1. **Closure under addition:** If...
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A **vector space** is a set of objects called **vectors** along with two operations—**vector addition** and **scalar multiplication**—that satisfy certain rules (axioms). Formally, a set over a field (like real numbers ℝ) is a vector space if: 1. **Closure under addition:** If , then . 2. **Commutativity of addition:** . 3. **Associativity of addition:** . 4. **Existence of zero vector:** There exists such that . 5. **Existence of additive inverse:** For each , there exists such that . 6. **Closure under scalar multiplication:** If and , then . 7. **Distributive laws:** - - 8. **Associativity of scalar multiplication:** . 9. **Multiplicative identity:** . **Example:** - (all 2D vectors with real components) is a vector space over . - Polynomials of degree ≤ n form a vector space. read less
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A vector space (also called a linear space) is a mathematical structure where vectors can be added together and multiplied by scalars, and the results still remain inside the same space.
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A vector space (also called a linear space) is a mathematical structure where vectors can be added together and multiplied by scalars, and the results still remain inside the same space. read less
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A vector space (also called a linear space) is a mathematical structure where vectors can be added together and multiplied by scalars, and the results still remain inside the same space.
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A vector space (also called a linear space) is a mathematical structure where vectors can be added together and multiplied by scalars, and the results still remain inside the same space. read less
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