"Vector Space
Description
A vector space is a collection of objects called vectors, which may be added together and multiplied by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. Wikipedia"
https://en.wikipedia.org/wiki/Vector_space
What is F in the Vector Space
"The general definition of a vector space allows scalars to be elements of any fixed field F. The notion is then known as an F–vector spaces or a vector space over F. A field is, essentially, a set of numbers possessing addition, subtraction, multiplication and division operations."
https://en.wikipedia.org/wiki/Vector_space
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"What is a span of a set of vectors?
The span of a set of vectors is the set of all linear combinations of the vectors. For example, if and then the span of v1 and v2 is the set of all vectors of the form sv1+tv2 for some scalars s and t. The span of a set of vectors in gives a subspace of .
Linear Algebra basics
https://www.rpi.edu › ~mitchj › handouts › linalg
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Gaussian elimination – Wikipedia
https://en.wikipedia.org › wiki › Gaussian_elimination
Gaussian elimination, also known as row reduction, is an algorithm in linear algebra for solving a system of linear equations. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients.
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https://en.wikipedia.org/wiki/Gaussian_elimination
Linear Maps
"In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (for example, two vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
Linear map – Wikipedia
https://en.wikipedia.org › wiki › Linear_map
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