Vector spaces are fundamental in linear algebra and are a collection of vectors that can be added together and multiplied ("scaled") by numbers, known as scalars in this context. This concept is key to understanding more complex topics in mathematics and are used in various applications including engineering, physics, computer science, and statistics.
In detail, a vector space over a field F is a set of elements known as vectors, together with an operation of addition, and an operation of scalar multiplication satisfying certain axioms like associativity, commutativity, the existence of an additive identity and inverses, etc.
Did you know? The concept of vector spaces extends beyond two or three dimensions to potentially infinite-dimensional spaces!