Common Application Of Linear Algebra In Sociology And Psychology

Common use of running(a) algebraAt the website 1 ) from the list below the following problem is presented : it is necessary to propose a amount in compliance with which one whitethorn select the strongest group basing on the results of the aggroup contest . At the website 2 ) some a nonher(prenominal) problem is presented Suppose we have an governance (e .g . business , sort of friends computer electronic network , and we emergency to keep track of how members (e .g departments , individuals , machines ) spread abroad with others . In both shields we can model the situation with a matrix of 0 s and 1 s . In the i-th row and j-th newspaper column of such the matrix we put 1 if the i-th Team get the better of j-th Team , or if the i-th Member of fundamental law communicates with the j-th Member of make-up without mediators . If the i-th Team defeated the j-th Team or the i-th Member of organization communicates with j-th Member of organization we claim that i-th chemical component has trip the light fantastic control over j-th office . If we add up all matrix chemical elements from the k-th raw , thus in the case of athletic competition we testament have the Team has will result or we will have the k-th member of organization with othersIf on that point are two teams which have the same number of victories over other teams whence we will face a question how to settle down which team is the surpass ? With this aim we may calculate trip the light fantastic toe dominances . For this purpose we have to calculate matrix A2 . It is truly unreserved to understand (moreover the detailed explanation is presented at the website 1 , that ij-th element of this matrix will show how many trip the light fantastic toe dominances the i-th team has over the j-th team . It is obvious that the sum of all elements in the i-th raw will show the number of two-step dominances of the i-th team over the all other teams . Thus , having two teams with the tinct number of victories (one-step dominance ) we can suppose that team to the beaver which will have greater number of two-step dominance Alternatively , one could count both one-step and two-step dominances by computing A A2 . The team with greater one-step and two-step dominances should be considered to be the best . With respect to members of organization i-th and j-th , the matrix A2 records the fact that A has two different routes of 2-stage confabulation with BSimilarly the content of elements of matrixes A3 , A4 , etc becomes apparentHowever , it is not so apparent how to use the methods of stage businessar algebra in the case when among the feasible results we may key out not only victory or defeat but in addition draw . In this case the method considered for defining the best team requires to be a little modifiedWe also may apply the methods of elongate algebra for plaining graphs Graphs are the objects which have analogies in everyday life . The websites 3 ) and 4 ) provide with world(a) idea of what a graph is Sociologists and psychologists use graphs to determine different kinds of relationships , such as influence , dominance , and communication , in groups . Graphs can be presented in the form of lines (called edges that connect points (called nodes . The application of graphs to the tasks of real life is very interestingGraphs can be very difficult , so that they cannot be visually analyzed To study such graphs it is necessary to use the methods of linear algebra . Thus , a graph may represent communications network where vertices , or nodes represent lecturers of telephone network and edges represent phone line . Two points may or may not be connected with phone line . The study of such a telephone line is very complicated task art object it may consists of thousands of subscribers . We may compose a matrix which will represent such a telephone line . In the i-th row and j-th column of this matrix we put 1 if at that place is a direct connection amid i-th and j-th subscriber , and 0 otherwiseNow we may face the question is it possible for a subscriber i to dig in the given telephone network the subscriber j ? After the analysis of the information presented at the websites 1 ) and4 , we can easily understand the way by which we may receive the answer to this questionIt s necessary to see whether the element of the matrix aij is compeer 0 or 1 . If it s partake 1 , and then the subscriber i can reach the subscriber j , if it s equal 0 , then we cannot range that the subscribers cannot reach each other over the telephone .

So we moldinessiness proceed to the second stepIt s necessary to obtain matrix A2 and find out whether the element in the i-th row and j-th column is equal 1 or 0 . If it s equal 1 , then the subscribers can reach each other . In case the element is equal 0 , then again we cannot assert that the subscribers cannot reach each other over the telephone . We must go on to the step threeIt is necessary to look for ij-th element of matrix A3 and so on till matrix An-1 , where n is the where k ?n . This may seem obvious , if we beak that the longest way by which the subscribers can be connected among themselves is that way when all other subscribers will be ordinary . This longest way will have the following appearancei-th j-th Its continuance is equal n-1Having constructed a graph for telephone network and the identical matrix we may ascertain is this network is integral or does it break into separate networks . We also may clarify whether there are defects in the network . However , if the connection between any subscribers can be executed directly not by the single way but by some(prenominal) ways as it is illustrated in the figure below then the given presentation of the graph needs certain adaptation It is obvious that these models are absolutely realistic and give us insights into dominance and similar phenomena . Using non-mathematical approaches it may be possible to understand such phenomena but it will take advantageously more time and efforts than it will when applying mathematics . The application of linear algebra may considerably simplify studies of certain phenomena and allow , with relatively few efforts receiving the answers to set questions1 ) HYPERLINK hypertext transfer protocol /media .pearsoncmg .com /aw /aw_lay_linearalg_3 /cs_apps /dominance .pdf br hypertext transfer protocol /media .pearsoncmg .com /aw /aw_lay_linearalg_3 /cs_apps /dominance .pdf2 ) HYPERLINK http /users .wpi .edu vadim /LA_I /Projects /project1 .html http /users .wpi .edu vadim /LA_I /Projects /project1 .html3 ) HYPERLINK http /aix1 .uottawa .ca jkhoury /graph .htm http /aix1 .uottawa .ca jkhoury /graph .htmp -p 9pabmh[wp mnpp AKLkhya brYp YUyuyapB_Bridges_of_K C3 B6nigsberg5 ) HYPERLINK http /www .math .uiowa .edu jsimon /COURSES /M10Fall04 /CommunicationAndDom inanceMatrices .pdf http /www .math .uiowa .edu jsimon /COURSES /M10Fall04 /CommunicationAndDomi nanceMatrices .pdf ...If you want to get a full essay, order it on our website: Orderessay

If you want to get a full essay, wisit our page: write my essay .