Linear algebra must find the meaning behind it. For the calculation of determinant, you should list it as an equivalent equation group and then solve the equation group step by step against the calculation process of determinant. You will know the meaning of determinant after solving it. To put it bluntly, it is a process of solving homogeneous linear equations, which junior high school students should know.

When learning vector, matrix and matrix multiplication in the future, we should know what their geometric meanings are and what they look like in the set space. For example, the vector is a line segment starting from zero, and the vector multiplied by the real number is the scaling of the line segment in geometric space without changing its original direction. Matrix is a set of linear transformation rules, and matrix multiplication is a given linear transformation applied to the target.

As for the specific transformation, you need to know the geometric meaning of the basis, and then there will be a lot of concepts such as eigenvalue, eigenvector and orthogonality. And you must understand their geometric meaning step by step and imagine them in the geometric space in your mind.

? Introduction to linear algebra;

Linear algebra is a branch of mathematics, and its research objects are vectors, vector spaces (or linear spaces), linear transformations and linear equations with finite dimensions. Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis; Through analytic geometry, linear algebra can be expressed concretely.

The theory of linear algebra has been extended to operator theory. Because the nonlinear model in scientific research can usually be approximated as a linear model, linear algebra is widely used in natural science and social science.