MATRICES:
Matrices are very useful tools that are widely used for their ability to represent in a helpful and concise way different mathematical objects, such as linear systems, which makes them a central tool of mathematics.
The students, divided into groups, have addressed several issues having to do with the use of matrices.
Quickort is an algorithm of recursive sorting in place that sets its base on the paradigm of “Divide et Impera”. The base of its working is the recursive use of the partition procedure: taken an element from a data structure we place the minor elements at its left and the major ones at its right… but how complex can this algorithm be?
Read MoreThe mergesort is a sorting algorithm based on comparisons that uses a process of recursive resolution, exploiting the technique of “Divide et Impera” consisting in the division of the problem in subproblems of the same nature of increasingly smaller size. In which cases is more convenient to use this type of sorting?
Read MoreThe Playfair cipher or Playfair’s square is an manual symmetric encryption technique and was the first literal Polyalphabetic cipher. The scheme was invented in 1854 by the English physician Sir Charles Wheatstone, but it is named after his friend Lord Playfair Baron of St. Andrews who tried to spread its use./p>
Read MoreAppIn classic cryptography, the Cipher of Hill is a Polyalphabetic substitution cipher based on linear algebra. Created by Lester S. Hill in 1929, it was the first Polyalphabetic cipher in which it was possible even practically (even if with some difficulties) to operate with more than 3 symbols per time.
Read MoreAppIn this article we will deal with the study of Gauss’ reduction method, that allows to transform every single squared matrix in the triangular or diagonal form. Transforming a matrix into the reduced form makes easier, for example, to solve a linear system.
Read MoreIn this article we will explain how to use the C++ technology to solve linear system, given by matrices of every dimension as long as they are squared.
Read MoreDownloadin this article we want to demonstrate how the method used to define if a linear system of two equation in two variables is determined, indeterminate or impossible can not be applied in order to solve a linear system of three equation in three variables.
Read MoreIn this article we will give the statement rod the theorem of Rouché – Capelli and we will use it, showing how to apply it, to revisit the linear systems and define their nature: if the system is impossible, determined or if it has infinite solutions and verify the grade of freedom of the infinite solutions. We will use the theorem of Rouché – Capelli.
Read MoreThe aim of this article is to think over the different application of the operations’ properties depending on the sets to which the terms of the operations belong. In particular we will compare the operations in the R set of real numbers and the ones of the M set of the matrices. We will take as example the difference in the resolution of equations with elements belonging with different sets, consequence of the fact that inside different sets the same theorems don’t always apply.
Read MoreIn the first part of this article will be showed the method to classify the conical through matrices associated to them, while in the second part the affinities will be used to transform the equation of a generic conical in the plan in its correspondent conical in canonic form..
Read MoreHow is it possible to exploit the potentialities of the matrices in the field of analytic geometry? The hundreds of facets applicable to matrices simplify and amplify the world of geometry. Here we deepen some examples of such applications.
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