Vector spaces

Question 1

What is a vector space?

Answer 1

A vector space is a set of vectors where addition and scalar multiplication are defined and satisfy properties like associativity, distributivity, and the existence of a zero vector.

Question 2

What are the key properties of a vector space?

Answer 2

Closure under addition and scalar multiplication.
Existence of a zero vector (additive identity).
Existence of additive inverses.
Distributive and associative properties for scalar and vector operations.