Review of linear algebra should pay attention to points of convergence and transformation of knowledge. As the various parts of linear algebra link between the very close, and over the years most of the exam questions are related to several parts of the content, so there must be a linear algebra review holistic awareness. Determinant and matrix is the foundation of knowledge, as well as vectors, equations, eigenvalue, etc. has been the examination center. Review should pay attention to the following points.
1, focusing on understanding and grasp basic concepts, correctly skilled in using the basic method and basic computing.
The concept of linear algebra are many important ones are: cofactor, adjoint matrix, inverse matrix, elementary transformations and elementary matrix of orthogonal transformation with the orthogonal matrix, rank (matrix, vector group, the second type), equivalent to ( matrix, vector group), linear combination and linear Biaochu, linear correlation and linear independence, a great group of linearly independent basic solutions of the Department and the general solution, solve the structure and solution space, eigenvalue and eigenvector, similar with similar diagonalization, the second type of standard form and normal form, positive definite, the contract transformation with the matrix of contracts.
Linear algebra algorithms and more should be finishing it clear not to confuse, basic computing and basic methods to cross the border, it is important are: determinant (digital type, letter-type) calculations, inverse matrix, find the rank of matrix, seeking phalanx the power, seeking the rank of vector group and a great group of linearly independent, linear, or seek to determine the relevant parameters, seeking the Department of Fundamental Solutions, seeking non-homogeneous linear equations of the general solution, find eigenvalue and eigenvector (as defined in the Law , characteristic polynomial-based solution of the Department of Law), to determine and demand similar to a diagonal matrix, with orthogonal transformation of real symmetric matrix is a diagonal matrix (that is, by orthogonal transformation of the second type is the standard form).
Second, pay attention to points of convergence and transformation of knowledge, knowledge into a network must strive to improve the comprehensive analysis capabilities.
Linear Algebra from the content point of view criss-cross, before and after the close-knit, interlocking and mutually penetrable, and therefore flexible problem-solving approach, review should be done often ask themselves, right? Ask well bad? Only by constantly to the summary, efforts to find out the internal links, so that what they have learned mastery, interface and entry point for much more familiar with, and thoughts naturally broadened.
For example: Let A be m × n matrix, B is n × s matrix, and AB = 0, then we can see with the sub-block matrix B, the column vectors are the homogeneous equations Ax = 0 of the solution, then according to the Department of Fundamental Solutions theory and the rank of matrix and vector group of rank relationships, there can be r (B) ≤ nr (A) or r (A) + r (B) ≤ n, and thus rectifiable matrix A or B, some of the parameters.
All of these, precisely because the knowledge of linear algebra between points are inextricably linked, algebra problems on a comprehensive and flexible large, we should pay attention to when finishing series, convergence and conversion.
Third, pay attention to logic and narrative statements
Linear Algebra for abstraction and logic higher requirements, through the proofs of the candidates to understand the main principles of mathematics, understanding and mastery of the theorem, examine the candidate’s ability to abstract thinking, logical reasoning abilities. We review order, it should find out the formula, theorem conditions, can not be wrongly tagged, and at the same time attention should be paid the narrative language expression should be accurate and concise.
It should be said PubMed easiest part is the mathematical linear algebra, this part of the difficulty lies in the concept are many and interrelated, but the line runs through the main line is the desire on behalf of the equations, as long as the equations of the concepts and general methods gain a thorough understanding, and then turn around and look at the content in front of the very simple. At the same time from the examination content point of view, the contents of the test substantially similar can be said that death is the most part, these last few years of examination questions before the exam is actually a replica, carefully researched look at before the exam is the most beneficial to everyone.
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