According to mathematical concepts

Linear algebra is a branch of mathematics about vector space and linear mapping.

Including the study of lines, surfaces and subspaces.

It also involves the general properties of all vector spaces.

Linear algebra is the core of pure mathematics and applied mathematics.

Its meaning expands with the development of mathematics.

Theories and methods have penetrated into many branches of mathematics.

It has also become an indispensable basic knowledge of algebra in theoretical physics and theoretical chemistry.

More importantly, linear algebra can be understood as a tool.

Through a set of established models and symbolic system, the mapping between grammar and semantics is completed.

It is very convenient to solve geometric problems in linear space.

In fact, the syntax and semantics of vectors, matrices and operation rules are all artificially designed.

From the application point of view, linear algebra is a domain-specific language (DSL) designed artificially.

The core of linear algebra is vector model.

Linearity, in layman's terms, means that there are only two operations on variables: multiplication and addition and subtraction.

Linear algebra has various important applications in mathematics, physics and technology.

Therefore, it occupies a primary position in all branches of algebra.

Nowadays, computers are widely used.

Computer graphics, computer aided design, cryptography, virtual reality and other technologies.

They all regard linear algebra as a part of their theoretical and algorithmic foundation.

Relationship between Geometric Concepts and Algebraic Methods in Linear Algebra

Axiomatic method abstracted from concrete concepts, strict logical deduction, ingenious induction and synthesis, etc.

When learning linear algebra

The most important thing is to master the concepts and algorithms of various matrices and vectors.

Determinant, matrix multiplication and inversion, etc., that is the most basic.