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Linear algebra (English: linear algebra) is a branch of mathematics about vector space and linear mapping. It includes the study of lines, surfaces and subspaces, and also involves the general properties of all vector spaces. Modern linear algebra has been extended to study arbitrary or infinite dimensional space. A vector space with dimension n is called an n-dimensional space. Most useful conclusions in 2D and 3D spaces can be extended to these high-dimensional spaces. Vector space (linear space), as a purely abstract concept used to prove theorems, is a part of abstract algebra and has been well integrated into this field. The set of all these transformations is itself a vector space.