To learn linear algebra, we must make clear the relationship and transformation between the parts, master the related concepts in linear algebra, understand the connotation of the concepts more deeply, and learn to master the contents of each part.
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.
Content of linear algebra
The first chapter mainly introduces the related contents of determinant, focusing on the concept, properties and calculation methods of determinant.
The second chapter mainly introduces the related contents of matrix, focusing on the concept and operation of matrix, the properties of determinant of square matrix, the concept and properties of inverse matrix and the elementary transformation of matrix.
The third chapter mainly introduces the related content of N-dimensional vector, focusing on the basic concept of vector group, the concept of linear correlation and its judgment, and the maximum linearly independent group.
The fourth chapter mainly introduces the related contents of linear equations, focusing on the structure of solutions of linear equations.
The fifth chapter mainly introduces the related contents of similar diagonalization, focusing on the definition and properties of similar matrix, the eigenvalues and eigenvectors of square matrix, the conditions of diagonalization of square matrix, diagonalization of real symmetric matrix and so on.
The sixth chapter mainly introduces the relevant contents of quadratic form, focusing on the concept and matrix representation of quadratic form, the standard form and standard form of quadratic form, and the concept and properties of positive definite quadratic form.