An Investigation into A Particular Operation on a Set of 100 Numbers Essay

An Investigation into A Particular Operation on a Set of 100 Numbers - Essay Example (Determinants and Cramer's Rule for Linear Equations, Undated) Both A and B are square matrices and thus the laws of determinants are applicable to them. Definition: There is no stand-alone definition of a determinant but it is defined in terms of a series of matrices as is evident hereafter. The determinant of an n x n matrix is defined as a sum of +/-1 times determinants of (n - 1) x (n - 1) matrices. (Determinants and Cramer's Rule for Linear Equations, Undated) Now that the technique of calculating determinants of matrices of any order has been somewhat explained a singular property of A is being touched upon. A's Singularity Any 2 x 2 matrix derived out of any set of numbers in adjacent rows and columns of A has the same determinant. Example: Suppose, E = 78 79 88 89 Then, DetE = (78 x 89) - (79 x 88) = 6942 - 6952 = - 10 This proves that all determinants of 2 x 2 matrices comprised of numbers in adjacent rows and columns are the same (-10) in the large 10 x 10 matrix A. This allows a general formula to be derived for the terms of all such matrices where N is a 2 x 2 matrix within A. N = n n+1 n+10 n+11 Here the numbers in the left diagonal - n and n+11 - have a periodicity of 11 while the numbers in the right diagonal - n+1 and n+10 - have a periodicity of 10. This is true of all 2 x 2 matrices comprised of numbers in adjacent rows and columns within A. And, detN = [n(n+11) - (n+1)(n+10)] = ( + 11n) - ( + 11n + 10) = - 10 This singularity gives rise to another that is mentioned in the calculations section and these two will make it easier to calculate the determinant of A... For an n x n matrix if the 'i' order row is considered and the (n-1) x (n-1) matrix derived by crossing out the row and the column is also considered then the determinant of the original n x n matrix is as below. For the matrix A it is noted that all values of , where 'i' is the 1st row and the matrix is a 2 x 2 one, is -20. It is considered for the essay that is the difference and not the true determinant value. This assumption is now being checked out in the essay for any term. Thus, for calculating the value of the determinant of A it is also found that the value ofis alternately negative starting with the second term. This makes it extremely easy to calculate the required value. Also, the operation has to be on a (n-1) x (n-1) matrix - a 9 x 9 matrix, as mentioned in the formula. This signifies that all numbers from 1-89 have to be considered. It is noticed on the right hand side of the equation that all even numbers are negative and all odd numbers are positive. Using the summation formula for series' in arithmetic progression - n/2[2a + (n - 1)d] - where n is the number of terms in the series, a is the first term and d is the common difference. (Arithmetic Series, MathWorld, 2006) The singularities revealed by the investigation allows us to determine that any square matrix of any order n x n constituted of the particular sequence of numbers belonging to the set of all positive numbers starti

Idea of translation and related issue Essay Example | Topics and Well Written Essays - 1250 words

Idea of translation and related issue - Essay Example That is why there is such an aspect as a misunderstanding or not understanding of the spoken or heard information. As the practice shows, such a thing as a pure translation is impossible. In any case there are some contributing factors such as the existence of opinions or attitudes to what is translated or interpreted by the person who translates, even some ethical or political reasons with the intention to influence the person who is aimed to hear the message, and so forth. So let’s see how the issue of translation is considered by different scientists – Emmanuel Levinas, Karl Marx in the context of the theme of colonialism and translation and whose ideas and statements are supported by Dr. Suh and whose ones are denounced by him. To begin with it is necessary to admit that both translation theories of Emmanuel Levinas as well as Karl Marx are linked with each other as the first one serves as a basis for the existence of the second one. We will start with Levinas who is well-known by his critics of the tradition of Western philosophical though. According to him â€Å"The sociality of language (or dialogue): cannot be reduced to the exchange of ideas between those who share the same ground of understanding and belong to the commonness† (Suh). So the theory of Levinas’s translation is attached with the main theme of ethical and political practice with the concepts of the â€Å"self† and the â€Å"other†, that is, â€Å"the problem of politics comes up because there are multiple others in the world† (Suh). Another important part in realizing of Levinas’s theory of translation is his concepts of the â€Å"saying† and the â€Å"said† – â€Å"The key t o connecting Levinas’s ethics to actual politics is understanding the relationship between saying and the said† (Suh). In other words, the â€Å"self† and the â€Å"other† have almost nothing common between them that’s