考研数学热点问答之线性代数篇（Ask of postgraduate mathematics linear algebra hot papers）

1、考研数学热点问答之线性代数篇（Ask of postgraduate mathematics linear algebra hot papers）The linear algebra section of the hot spot question,.Txt what is myth? Listen to men express love to you. What is the legend? Listen to the mans promise to you. What is a dream? See how you react when you hear the first two. 20

2、04 graduate mathematics hot quiz linear algebra chapter1., I feel linear algebra is still relatively difficult, in the end this month should be how to review it?Answer: This is a course of the most abstract, between this course each album is closely linked, linear algebra, this place is hard to say,

3、 while other courses in higher mathematics can be a separate chapter proposition, so linear algebra general questions andIn front of the knowledge closely linked, if the basic content is not good if this part of the time, this time I want to have a little time to tense, you re too late to review sys

4、tem, grasp some key problems by doing, look at those important theorems, important conclusions are not sure.2. how to cultivate the sense of wholeness in the review of linear algebra?Answer: the links between the chapters of a linear algebra are very closely related. What is the center of the thing,

5、 the determinant, the matrix, and the vector? This part is not determinant what you know is the main determinant determinant of the meaning, nature and so on, is the key determinant, the determinant of the R party, this problem is an important formula. A matrix A multiplied by the adjoint matrix of

6、A is equal to the determinant of A multiplied by a unit matrix, and this formula is the way of expansion of our determinant R square matrix. Each chapter has links, so when you review, you should focus on the chapters.Determinant has nothing, the second chapter matrix, the matrix is a basis, related

7、 to the entire line generation, so the operation of the matrix is very important, especially do not do illegal computing. Because we are used to the operation of the number, in doing matrix operation, easily affected by the number, so this place we should make it clear. A very important element in m

8、atrix operations is elementary transformation. Were solving equations, and were looking for things that feature vectors cant be separated from. This is the focus of our matrix section.This part is the logical vector is very strong, we also feel more difficult, this part of the logical reasoning is v

9、ery strong, we must be very familiar with the teaching materials in important theorem to get a problem immediately to reflect. For example, such a theorem, many candidates feel that this theorem is difficult, in fact, can be vividly recorded. Of course, the first vector group is represented by secon

10、d vectors, the second vectors are linearly independent, and the first vector group can be derived. The number of vectors containing less than second vectors contains the number of vectors. This theorem has been tested many times. In 2003, it was a multiple-choice question. In fact, this problem we c

11、an change a way down, for example, I used this to remember, that is a linear independent vector group may not have a less than his number of the linear vector group said that this sentence is expressed in our previous theorem. It is intuitive geometric refers to a high dimensional space that cant be

12、 put in low dimensional space, at least in the same space. For example, a solid object can not be placed in a flat surface and can not be placed in a straight line. After you have understood the geometry in such a way, the theorem will not be mistaken.In the system of equations, the three parts are

13、the determination of the solution, the nature of the solution and the structure of the solution. Another is the eigenvalues and eigenvectors. For the eigenvalue, you can solve a specific equation for the specific one. The eigenvector is the fundamental solution to the system of homogeneous equations

14、, and the foundation in front of you is secure, and this is not new. The content of the two type, for those who only test mathematics, mathematics three, the two type, as long as the corresponding matrix is written out, the problem can be transformed into symmetrical matrix diagonal type to discuss.

15、 So the contents of the back are linked to the front. Lay the foundation of the front, and the knowledge behind you is mastered.Or linear algebra encountered the problem of analysis, and sometimes the problem of the matrix into linear equations to do, and sometimes the linear equations of the proble

16、m into a matrix to solve. If we refer to a vector as another vector in the problem solving process, we can substitute the other vector with the unit vector, so that we can get the result quickly. Another point is the eigenvalues and eigenvectors of the square, which should be noticed by a large numb

17、er of graduate scholars. This is the focus of our linear algebra, and it must be a big problem every year.3. what problems should we pay attention to in the review of linear algebra?Answer: We PubMed, especially in this part of linear algebra review should pay attention to what issues?. In compariso

18、n with advanced mathematics and probability statistics, we often feel that linear algebra has more concepts, more formulas, and more conclusions. There is knowledge has particularly close ties, but the mathematics of one to four in fact we now the linear algebra questions have been defined, a mathem

19、atical test five to four questions, in the choice of three, the remaining two questions, the content is actually just three blocks: row column matrix can be regarded as the basis linear algebra, such words are the basis for the future, vector and linear equations can be regarded as the same thing in

20、 two different forms, another two times, only one and three do the math. Around such a vector and linear equations, the basic exam every year a big problem. Around the vector and the two type, in some sense, will also be seen as the same thing in two different aspects, each year to test a big proble

21、m. Mathematics two and four do not require the two type, around the special vector is basically a big exam. This is the general outline of our entire linear algebra. We hope that when you review, you should have targeted the matrix and determinant of this foundation to play well. Then make clear the

22、 typical cases of our vectors and linear equations. Targeted, systematic induction and summary. So regardless of the test questions or multiple-choice test or examination, the question out basically we can clear judgment, get this question what is typical I can analysis of the ideas, which is a typi

23、cal method can solve the. In the middle of the question making process, are there some skills such as the corresponding question making skills? Are there any hidden conditions that should be noticed?. In this case, after we grasp it in general, we can find a relatively simple, fast and accurate solu

24、tion to this problem. Now, Im happy to answer some specific questions.4. I would like to ask what are the main applications of elementary transformation?Answer: is the foundation of our matrix problem, elementary transformation vectors can rank, we often can solve equations, here is often the studen

25、ts confused, we inverse in general we construct this matrix is a matrix on the right side, we emphasize the transformation, the solution of linear equations when we to consider the linear matrix and rank, simple matrix or vector group that can be done for the rank transform can do column transformat

26、ion. If we take this as a vector set of column vectors of matrix, not only for the rest of the vector also rank linear representation, in fact linear representation is the essence of the solution of equations, so we generally try to elementary transformation to habit.5., is the probability of the re

27、levance of vectors very high in the proof questions of linear algebra?Answer: linear correlation and linear independence from the test situation, you can directly test, sometimes indirect test, for example to prove the basic solution, we refer to this set of vectors must be linearly independent, its

28、 required to prove that linear independence, it should be said that this is the basis of comparison of linear algebra the problem, this situation is not necessarily directly admitted to you, of course can also direct examination,But, in terms of our linear equations, and we combine the vectors behin

29、d, for example, the eigenvectors of different eigenvalues, it is also a typical form of expression in this form, which we must master.6. I was admitted to feeling three contract transformation concept more difficult to understand, ask the teacher generally talk about?Answer: the contract is for the

30、two time we transform type of intermediate process to the standard form we will introduce a so-called non degenerate linear transformation, i.e. a transformation matrix that we must be reversible, so I put the two type of time through the standard form, I will find the two type into standard form is

31、 converted to two new matrix when it corresponds, this time is equal to the diagonal matrix, but generally we find a non degenerate matrix, not necessarily just equal to a diagonal matrix, if you meet such a condition, we define this the two matrix is the contract, like diagonalization, matrix AP th

32、at is equal to a diagonal are equal, but under normal circumstances is not necessarily a diagonal matrix, we say that the two are similar. So if only from the contract transformation leads to contract matrix itself, it should be said that this concept is not particularly difficult to understand, but

33、 we should pay attention to the review, I have the concept of the contract after the contract matrix matrix, it satisfies the corresponding properties, from this perspective can better grasp, three the most typical relationship between the linear algebra matrix: a matrix similar to two, a two matrix

34、 equivalence, and the matrix of the two contract, should pay attention to the relationship and difference between the two, I think the relationship between the three actually equivalence relation is a matter of the weakest. Is similar to the two matrix, two matrix contract, the two matrix must be eq

35、uivalent, but the converse is not true. Similarity and contract matrices can not be deduced from each other. But if the two real symmetric matrices are similar, then it must be the contract. That is to say from the whole matrix has three kinds of relations, relations and differences of these three k

36、inds of relations inside if I just say this from several angles to grasp, I think no matter what we are matrix, to better understand and grasp.7. linear algebra can be combined with some of the higher mathematics knowledge point of the question? Is there any possibility of such a test?A: since the r

37、evision of the general outline in 1997, since 1998, each year has been involved in the cross cutting of three subjects, and the volume will not be too large to do so. For example, our most simple linear algebra inside through determinant determinant, we can define a function, it can function on high

38、er mathematics all the examination of the contents of a function defined by the determinant, the determinant of the nature of the determinant of the concept, calculation and higher number of examination function characteristics, function limit, derivative and integral will combined test. In addition

39、 to our linear algebra vector, such as inside the matrix, the two type head may be here with a random variable, we can get the probability of random variables, as long as the usual review of little note can, there is no need for special review.8. the teacher for advice if there is some candidates in

40、 2004, the remaining few days sprint and quality improvement? Where do you think the whole of linear algebra is? Where is the breakthrough point for learning?Answer: the answer to this question, in fact we consider to the proposition of the students should be a bit clearer, we refer to this question

41、 is to fill in the blanks, selection, calculation and proof, this design has his consideration, fill in the blanks is to test the knowledge points, examination outline any knowledge may test your questions, but absolutely no calculation is very complicated, so dont expect where is the key, in fact o

42、ften fill in on what you think is not easy to place or not out of the question, but he would probably be a simple questions such as,I hope our classmates must make a comprehensive and systematic review. For example, the calculation of the average function, these are some relatively isolated, relativ

43、ely isolated points of knowledge, but you will fill in the blanks. Selective test, comparative analysis, judgment ability. The calculations show that we consider the flexibility of our thinking and the flexibility of our existing knowledge. So in this case, often will be a number of knowledge points

44、 in a problem reflected. I feel that if I expect mathematics two days later, there was a breakthrough in essence, may be more difficult, but at the end of this period of time for us to make good use of the whole score remained stable, and even have a relatively large increase is entirely possible. S

45、ome of our classmates begin to spend a lot of time reviewing math. At last, they have both specialized courses and political theories. They need to put a little more emphasis on the past If you do not do something for a period of time, suddenly doing it, feeling very strange, so the last period of t

46、ime inside, do not say I used to review good, I put a put, do not have this idea. Mathematics problems really score from 100 points to 150 points, after the success of the postgraduate entrance examination, the impact is very great. The last stage of breakthrough and improvement, this can be achieve

47、d through simulation training, we usually are relatively fragmented review a knowledge point, this last stage is able to improve break through the use of simulation that good, do simulation training, the simulation training is what I just said should be specified in the time inside, then must sum up

48、. I hope we each students do a set of questions, each summary again can have a raise, you continue to find the problem, actually what things are so Practice makes perfect. we compiled simulation problem, it also has to consider the general difficulty, may be less than the actual exam is too difficul

49、t, second coverage, third students prone to problems the place to dig out, you can use very high simulation questions. We designed 15 sets of questions, we hope that the students finish within one month, so eventually all finished, and each finished according to our design idea of the summary, I bel

50、ieve that our students will have a breakthrough. Asked to focus on linear algebra, linear algebra questions I hope our students pay attention, do not talk to the key and non key, multiple-choice test concept comparison, test analysis and judgment ability, often specious concept mixed together, is ma

51、inly the concept of some subtle differences between you clearly dont know, so if we focus on to say the key, especially the big question, I think it is quite clear that every year will certainly be around vector and linear equations on a big problem, the second is the special vector, will be combine

52、d with the two type test, the two test block is the most, other places are not absolute big problem but relatively speaking to say your focus and I think the two block is the most important.9. what is the difference between the choice of transformation matrices in terms of real and non real symmetry

53、?Answer: if a simple diagonalization, there is no difference in the nature of real symmetric and non symmetric, real symmetric matrix is ordinary matrix, so you only as long as it is diagonalized, you can always find the vector, and then constructed a reversible against, I can find a special vector

54、to construct a him. Invertible matrix diagonalization, making them. But the real symmetric matrix has better properties than the general matrix, if you put the same feature vector diagonalization, and then put all feature vectors together units, this time you will find a reversible matrix, the diago

55、nalization, and it can also guarantee that the invertible matrix is a diagonal.10. ask teacher algebra how many points?Answer: we are math one, math two, algebra 20, math three or four is 25%.11., the concept of linear algebra is more, how to review more appropriate?Answer: as a conceptual thing,The

56、 first step is to understand the meaning of knowledge, you simply put this concept back down may be no problem to back down, but you really want to understand it, or to master it, one of the best mathematical concepts, grasp and understand the concept of the way I think is to solve the problems, we

57、often do not do is because I didnt have a good understanding of the concept of time, back to look at the concept, the concept of understanding is deepened step by doing a better approach is to grasp the concept of.12. ask the teacher to pledge the topic of this years line generation.Answer: the so-c

58、alled math charge, mathematical questions form is very flexible, so it should be said that in each case it can be linked to this problem, the so-called charge can also be considered, such as the determinant calculation can not be set, you can think of it, combined with the matrix operation test a de

59、terminant calculation problem, we can also find test the determinant calculation by the eigenvalue, with similar matrix determinant calculation test, the test form, so far which pass the test, using the knowledge on determinant determinant calculation is not passed, the next step is not to test? In fact, from the questions in the form of speaking is the combination of test matrix determinant determinant, then it is to test the determinant calculation by this form of que