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Besides these basic concepts, linear algebra also studies vector spaces with additional structure, such as an inner product. The inner product is an example of a bilinear form , and it gives the vector space a geometric structure by allowing for the definition of length and angles.
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations
Functions – mapping that associates a single output value with each input value; Sequences – ordered list of elements either finite or infinite; Systems of equations – finite set of equations; Vectors – element of a vector space; Matrix – two dimensional array of numbers; Vector space – basic algebraic structure of linear algebra
The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group. Outline of algebra; Glossary of field theory; Glossary of group theory; Glossary of linear algebra; Glossary of ring theory; List of abstract algebra topics; List of algebraic structures
Linear systems are a fundamental part of linear algebra, a subject used in most modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics.
For many problems in applied linear algebra, it is useful to adopt the perspective of a matrix as being a concatenation of column vectors. For example, when solving the linear system =, rather than understanding x as the product of with b, it is helpful to think of x as the vector of coefficients in the linear expansion of b in the basis formed by the columns of A.
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