First, basically pass the customs.
Shenyang Haitian Postgraduate Entrance Examination Leap Plan thinks that there are many concepts of line generation, including algebraic cofactor, adjoint matrix, inverse matrix, elementary transformation and elementary matrix, orthogonal transformation and orthogonal matrix, rank (matrix, vector group, quadratic form), equivalence (matrix, vector group), linear combination and linear representation, linear correlation and linear independence, maximal linear independence group, basic solution system and general solution, solution structure and solution space. Shenyang Haitian Postgraduate Entrance Examination Leap Plan thinks that there are also many algorithms that must be mastered: the calculation of determinant (number type and letter type), the calculation of inverse matrix, the calculation of matrix rank, the calculation of power of square matrix, the determination of the rank of vector group independent of maximum linearity, the determination of linear correlation or the calculation of parameters, the calculation of basic solution system, the general solution of non-homogeneous linear equations, the calculation of eigenvalues and eigenvectors (definition method and basic solution system method of characteristic polynomial), and the calculation of characteristic polynomial.
Second, strengthen the ability of abstraction and reasoning.
Shenyang Haitian Postgraduate Entrance Examination Leap Plan holds that linear algebra requires students' abstract and logical abilities. The outline requirements mainly include the calculation of abstract determinant, the inversion of abstract matrix, the rank of abstract matrix, the eigenvalue and eigenvector of abstract determinant. Shenyang Haitian Postgraduate Entrance Examination Leap Plan thinks that these four abstract problems are also common problems in linear algebra every year, accounting for a large proportion. In addition to reasoning, Shenyang Haitian Postgraduate Entrance Examination Leap Plan thinks that linear algebra is a jumping reasoning process, which will be obvious when doing the problem. Shenyang Haitian Postgraduate Entrance Examination Leap Plan suggests that candidates should wait for the mathematical formula one by one from the first step to the second step to the third step when doing the problems of advanced mathematics. However, Shenyang Haitian Postgraduate Entrance Examination Leap Plan thinks that students often can't see the mathematical formula from the first step to the second step to the third step when doing the problems of linear algebra, such as the calculation of determinant, and it is often difficult to see from which line (or column) to which line (or column). Shenyang Haitian Postgraduate Entrance Examination Leap Plan believes that this requires students not only to firmly grasp the basic knowledge, but also to exercise abstract and reasoning skills.
Third, overall improvement.
Linear algebra is closely related to each other in content, so the leap plan of Shenyang Haitian Postgraduate Entrance Examination thinks that the method of solving problems is flexible and changeable, and the leap plan of Shenyang Haitian Postgraduate Entrance Examination requires candidates to always ask themselves whether they have done it right or not when reviewing. One more question, okay? Shenyang Haitian Postgraduate Entrance Examination Leap Plan holds that only by constantly summing up and trying to figure out the internal relations can we integrate what we have learned, become more familiar with the interface and entry point, and naturally broaden our thinking. For example, if A is an m×n matrix, B is an n×s matrix, and AB=0, then we can know that the column vectors of B are all solutions of the homogeneous equation Ax=0. According to the theory of basic solution system and the relationship between the rank of matrix and the rank of vector group, r(B)≤n-r(A) means R (a)+R (b) ≤ For example, Shenyang Haitian's Leap Plan for Postgraduate Entrance Examination thinks that it is because of the inextricable relationship between the knowledge points generated by lines that algebra problems are comprehensive and flexible. Shenyang Haitian Postgraduate Entrance Examination Leap Plan requires candidates to pay attention to series, connection and transformation when reviewing, so as to improve in an all-round way.