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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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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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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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Vector space is a set of elements, which can be added together or multiplied.
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A vector space is a set of vectors that can be added together and scaled (multiplied by numbers), while satisfying certain properties like closure, commutativity, associativity, and distributivity.
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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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