S is a subset of vector space v (attached to volume f). The set composed of all linear combinations of S is called the space spanned by S, and is denoted as span(S).

After introducing the concept of vector into analytic geometry, many problems are handled more concisely. On this basis, the concept of vector space associated with domain is further abstracted. For example, the polynomial set of real coefficients forms a vector space after defining appropriate operations, which is convenient for algebraic processing.

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The meaning of linear algebra is expanding with the development of mathematics. The theory and method of linear algebra has penetrated into many branches of mathematics, and it is also an indispensable basic knowledge of algebra in theoretical physics and theoretical chemistry.

It is natural for people to deal with many math problems. The treatment of many practical problems often comes down to linear problems, which are easier to deal with. Therefore, linear algebra is widely used in many fields of engineering technology and national economy, and it is a basic and important subject.

Baidu encyclopedia-linear algebra