Branches of Mathematics
Linear Algebra
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Linear algebra is the branch of mathematics concerned with linear equations, linear maps, and their representations in vector spaces and through matrices.
Facts
Central QuestionGiven a linear map between vector spaces, is it an isomorphism, and if not, what are its range and its kernel, the elements it sends to zero. 1 Key DebateWhether linear algebra is best understood through its original nineteenth century form, concrete computation with systems of equations, determinants and matrices, or through the abstract axiomatic vector space that only unified those techniques decades later. The field's basic results and techniques were developed and used for perhaps a hundred years before mathematicians even defined an abstract vector space. 1 Cross-Tradition Connections
Sources
1. Linear Algebra (Wikipedia)
Wikipedialead paragraphQuote, lead paragraph
Linear algebra is the branch of mathematics concerning linear equations such as a1x1+...+anxn=b, linear maps ..., and their representations in vector spaces and through matrices.
1. Linear Algebra (Wikipedia)
WikipediaLinear maps sectionQuote, Linear maps section
An essential question in linear algebra is testing whether a linear map is an isomorphism or not, and, if it is not an isomorphism, finding its range (or image) and the set of elements that are mapped to the zero vector.
1. Linear Algebra (Wikipedia)
WikipediaHistory sectionQuote, History section
The leading mathematicians of the nineteenth and early twentieth centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, without even defining an abstract vector space.
Vector Space (Wikipedia)
Wikimedia FoundationIncludes: Vector Space, lead paragraphQuote, Includes: Vector Space, lead paragraph
The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector spaces.
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