The first section N-order determinant one. Mathematical Concepts
1. Number of reverse order
For n different elements, we first specify a standard order between the elements (for example, n a different natural number, can be specified from small to large for the standard order), so in any of these n elements in any arrangement, when a certain two elements of the order and standard order is not the same, said there are 1 reverse. The total number of all
Topic Link:https://uva.onlinejudge.org/index.php?option=com_onlinejudgeitemid=8page=show_problem problem=625Test instructions: An n-order determinant is given, and the value is evaluated.Idea: Template reference http://blog.csdn.net/zhoufenqin/article/details/7779707:the nature of the N-Step determinant:Property 1: The determinant is equal to his transpose determinant
1. Mathematical DefinitionsThe N-step determinant is defined as follows:
2. Algorithm implementationFunction name: GetValue ()Function: Returns the value of a determinant Private FunctionGetValue ()DimGvalue as Double DimTempresultlist as NewList ( ofArray)DimTempnumarray (Ranklength-1) as Integer 'to make a sequence of all permutations fori =0 toRanklength-1Tempnumarray (i) =INextg
Today, using array pointers to rewrite the determinant of the program, Code:1#include 2#include 3 using namespacestd;4 intMain ()5 {6 intrank;7 voidSetdet (Double*,int);8 DoubleValdet (Double*,int);9cout"Enter the order of the determinant:";TenCin>>rank; One Double*detptr=New Double[rank*rank]; A Setdet (Detptr,rank); -cout"the determinant values
Ultraviolet A 684-integral Determinant Question Link Question: Give a determinant and find the value. Train of Thought: Use the column subtraction in linear algebra, and then continuously reduce the order, that is, use the score to write Code: # Include
Section 4 nature of the determinant
There are seven attributes of the determinant:
Order n determinant:
If you change the row of D to A column, the new criterion is as follows:
, DeterminantDT(Or D ') is called the deciding factorDThe transpose deciding factor.
Note: The transpose deciding factor can also be seen as the result of turning 180 ° with the primary di
Axiomatic definition of determinantGenerally speaking linear algebra, first of all, The matrix theory, and then the determinant, and then the linear transformation, linear space, eigenvalue theory, two-dimensional theory, and some domestic teaching materials such as the sixth edition of "linear algebra" first said the determinant of the matrix theory, simply anti-human, hehe. Recommended Use-Professor Gilbe
Chapter 1 determining factors
§ 1 second-and third-order Determinant ----------------> concept of the determinant2 full sorting and Reverse Order§ 3 Definition of the rank-N Criterion§ 4 interchange --------------------------------> the nature and calculation of the determinant§ 5 nature of the determinant§ 6 determine the number of rows (columns ).§ 7 karat Mo's
To undertake the introduction of the determinant of the previous article, this article will further record about the determinant of the relevant content, including the following aspects:(1) The proof of the Determinant 3 elementary transformations.(2) The proof that the determinant is equal to the original
When you use the MathType formula Editor to edit formulas, there is a need to be aware of them in the determinant layout, and this tutorial will explain the determinant of the typographic rules .In the determinant, the horizontal is called the row, and the vertical row is called the column. Its number of rows and columns is to wait, and the
component function. The Jacobi matrix is the derivative of the vector-valued function \ (f\) at the \ (x\) point: \ (\delta y=\textbf{f} (X_0+\delta x)-\textbf{f} (X_0) =a\delta X+\textbf{o} (\delta x), \ Qquad a=j\textbf{f} (x_0) \) "Jacobi determinant" If the vector value function \ (m=n\), then the determinant of its Jacobi matrix is the Jacobi determinant,
Section 1 second-and third-order Determinant
Before introducing the concept of determining factors, we first construct a math: place the four numbers on the four corners of a square, and add two vertical bars. That is to say, this toy corresponds to a result: the difference between the product of numbers on two diagonal lines. That is
For example
The diagonal line in the direction is called the main diagonal line, and the diagonal line in the directio
This chapter begins with an introduction to another basic concept in linear algebra-the determinant.In fact, like the Matrix, the determinant is also a tool for simplifying the expression polynomial, about the historical origin of the determinant, as the following introduction.In introducing the inverse matrix, we have mentioned that the second-order matrix has a corresponding
#include"stdafx.h"#include#include#include#defineNUM 3intFun (intNintA[num][num]);/*function Declaration*/intMain () {inti =0, j =0;/*i,j represents rows and columns, respectively*/ inta[3][3] = { { -,6,2},{6,3,3},{5,9,8} };/*Defining determinant*/printf ("%d\n", Fun (NUM, a)); System ("Pause"); return 0;}/*The following is a recursive function for calculating determinant values*/intFun (intNintA[num][nu
relationship between eigenvalues of matrices and determinant and trace
From:http://www.cnblogs.com/andyjee/p/3737592.htmlThe product of eigenvalues of matrices equals the determinant of matrices The sum of the eigenvalues of the matrices equals the traces of the matrices
The simple understanding proves as follows: the Vedic theorem of 1, two quadratic equations:
Think about this: x^2+bx+c=0 the sum of al
Determinant typeDeterminant in mathematics, is a function that defines the field as a Det matrix A, takes a scalar, writes Det (a) or | A |. The determinant can be seen as a generalization of the concept of a direction area or volume in a general Euclidean space. Or, in n-dimensional Euclidean space, the determinant describes the effect of a linear transformation
It's been a long time since I wrote C, and today I wrote a matrix algorithm.The complete code is as follows:#include #include#includestring>using namespacestd;//Create a matrixfloat**creat (intN) { float**array=New float*[n]; for(intI=0; i) {Array[i]=New float[n]; } printf ("Please enter the matrix: \ n"); for(intI=0; i) { for(intj=0; j) {cin>>Array[i][j]; } } returnArray;}//to find the determinant value:floatValue (float**array,
area retains 3 decimal places.Sample inputRectangle 0.0 0.0 1.0 2.0Circle 0.0 0.0 1.0Triangle 0.0 0.0 1.0 1.0 1.0 0.0Rectangle 0.0 0.0 1.0 1.0Circle 0.0 0.0 2.0Sample outputCircle2 12.566Circle1 3.142Rectangle1 2.000Rectangle2 1.000Triangle1 0.500ExercisesSince the calculation of the Helen formula will have errors, we use the second-order determinant to calculate the area of the triangle:Set A (X1,y1), B (X2,y2), C (X3,Y3) in the coordinate system in
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