dragonbox algebra

is divided into two steps: Judging the legality of two matrices; The K line of the A matrix is extracted and multiplied by the column I of the b Matrix, and the first column I of the target matrix is obtained. The following two kinds of writing are the above ideas, the first one faster, occupy less memory, the second closer to People's thinking (the second folding please expand).Template Matrixoperator* (matrix//operator Overloading * Overloading for point multiplication{ /

Reference: "Linear algebra" Tongji University, fourth edition 1. Elementary transformations of matrices 1) definition 2) equivalence relationship between matrices: definition, Nature (3) 3) row ladder-shaped matrix; the simplest form; standard type; equivalence class 2. Elementary matrices 1) definition 2) Theorem 1 (Relationship between elementary transformation and elementary matrix) 3) theorem 2 (the necessary and sufficient conditions for

Reference: Hiraoka and luckily Programmer's Math 3: linear algebra. 1. Vector-- What is the space 1.1 vector? Vectors, which can be seen as a pile of permutations.In space, a vector can represent a point, for example (2,3) that represents a point with a horizontal axis of 2 on a two-dimensional plane, an ordinate of 3, or a directed segment that points to it from the origin.When emphasizing the concept of "permutation number", it is generally indicate

The MIT Challenge My friend Scott Young recently finished a astounding Feat:he completed all the courses in MIT's fabled computer science C Urriculum, from Linear Algebra to Theory of computation, in less than one year. More importantly, he does it all in his own, watching the lectures online and evaluating himself using the actual exams. (see Scott's FAQ page for the details about how he ran this challenge.) That works out to around 1 course every 1.

3 31 2 4 % % The basis of zero space: the Code of this zero space is worth looking at, reflecting the basic idea of column meaning in linear algebra. You may not know what the code is. A simple statement may contain many operations. I like to give an example when I don't quite understand it. Let's take a look at the code in one sentence. Note that The column in the zero space indicates the linear combination of columns in the matrix that constitute t

- voidInsert (Char*R) { About intLen=strlen (s), p=RT; $ for(intI=0; i) - if(Ch[p][id (S[i])) -p=Ch[p][id (S[i]); - Else AP=ch[p][id (S[i])]=++CNT; +tag[p]=true; the } - $ voidBuild () { thequeueint>Q; the for(intI=0;i4; i++) the if(Ch[rt][i]) thefail[ch[rt][i]]=Rt,q.push (Ch[rt][i]); - Else inch[rt][i]=RT; the the while(!Q.empty ()) { About intx=Q.front (); Q.pop (); th

[find (1)]!=1){ thememset (Vis,0,sizeof(VIS)); num=0; the for(intI=2; i1; i++){94 if(Vis[find (i)])Continue; theVis[find (i)]=++num; the } thenum=0;98 for(intI=2; i1; i++) Aboutnum=num*Ten+Vis[find (i)]; -a.mat[id[num]][id[mem[t]]]+=1;101 }102 }103 }104 return; the }106 107 intMain () {108 #ifndef Online_judge109Freopen ("count.in","R", stdin); theFreopen ("Count.out","W", stdout);111 #endif thesc

1. Determinant1.1 Second-order determinant1.2 third-order determinant1.3 Number of reverse order1.4 N-Step determinant2. The nature of the determinantProperty 1 The determinant is equal to its transpose determinant.Property 2 swaps the determinant of two rows (columns), determinant.Property 3 The determinant of a row (column) in which all elements are multiplied by the same multiplier K, equals the number k multiplied by this determinant.Property 4 Determinant If there are two rows (column) elem

transformation.Matrix elimination Element Method:determinant TypeCalculation (0 descending order method)Other properties of the determinant:The law of ClydeMatrixFollow the law1. Linear Properties2. Operational and polynomial of n-order matricesElementary matrix and its role in multiplicationFor the unit matrix, the matrix obtained by making an elementary transformation becomes the elementary matrix.Together there are three primary transformations:The block rule of multiplication:Two frequently

Representation of graphs Adjacency Matrix Correlation matrix (horizontal longitudinal point, direction Graph 1 in-1 The connectivity of graphs Non-Tourienton/non-connected Forward graph strong connectivity/single-sided connectivity/weak connectivity Proof method: Specific analysis of the special case of the Reach matrix (Eulerian graph has the necessary and sufficient conditions, Hamilton full/essential Euler

1. Determinant 1.1 Second and third-order determinantSecond-order determinant = A * D-b * C　　　　Third-order determinant = A11*a22*a33+a12*a23*a31+a13*a21*a32-a31*a22*a13-a32*a23*a11-a33*a21*a12Three lines minus three lines1.2 full rank and reverse order numberAll-in-all arrangement: 1,3,2 2,1,3 2,3,1 3,1,2 3,2,1The total number of permutations is: 3*2*1 = 3!reverse order Number: Two elements of the size and position of the relationship does not match and there is an inverse (the general default f

] ofRec; V:Array[0..2002000] ofBoolean; N,m,i,j,k,l,st,ed,ww,top,tar,ans,x:longint;functionmin (aa,bb:longint): Longint;begin ifAa Thenexit (AA); exit (BB);End;procedureAdd (st,ed,ww:longint);beginInc (top); A[TOP].S:=St; A[TOP].E:=Ed; A[TOP].W:=ww; A[top].next:=B[st]; B[ST]:=top;End;functionBfs:boolean;varHead,tail,x,u:longint; Y:rec;beginFillchar (v,sizeof (v), false); Tail:=1; head:=0; d[st]:=1; V[ST]:=true; q[1]:=St; whileHead Do beginInc (head); x:=Q[head]; U:=B[x]; whileU>0 Do begi

1.The calculate the slope:the covariance of X and Y divided by the variance of X　　From NumPy import CoVslope_density = CoV (wine_quality["quality"],wine_quality["density"]) [0,1]/wine_quality["Density"].var () #cov ( X, y) is the function from NumPy, which returns a 2*2 Metric,.var () is Pandas function.2.To get the INTERCEPT:B = Y-ax (x and Y is the mean value of each column)Intercept_density = wine_quality["Quality"].mean ()-wine_quality["Density"].mean () * (Calc_slope (wine_quality[) Density

Topic Link: PortalTest instructionsGiven your three numbers, P,q,n, p stands for a + B, Q for a*b;Then ask A^n + b^nset F[i] = A^i +b^i; f[0]=2,f[1]=p;f[i]* (a+b) = a^ (i+1) + b^ (i+1) +a^i*b + b^i*a;F[i]*p = f[i+1] + a*b*[ a^ (i-1) + b^ (i-1) ]F[i+1] = f[i]*p + q*f[i-1];And then use the matrix to speed up a bit (PS. The input of this problem is very pit .... ）The code is as follows:#include UVA 10655 contemplation! Algebra (Matrix fast Power)

[Problem 2015s02] set \ (a,b,c\) is plural and \ (bc\neq 0\), proving that the following \ (n\) Order matrix \ (a\) can be diagonalization:\[a=\begin{pmatrix} A B \ C A B \ C A am P B \ \ddots \ddots \ddots \ C A b\\ C A \end{pmatrix}.\][Question 2015S02] Fudan Advanced Algebra II (Level 14) weekly (second teaching week)

[Linear algebra] matrix addition 1 # Include 2 Using Namespace STD; 3 4 5 Int Main () 6 { 7 Int Matrixa [ 100 ] [ 100 ]; // Matrixa 8 Int Matrixb [ 100 ] [ 100 ]; // Matrixb 9 Int Plusresult [ 100 ] [ 100 ]; // Matrixa + matrixb = plusresult (this is a maxtrix) 10 Int M, N; 11 Cout " Enter the required and number of rows and columns in the matrix. " 12 Cin> m> N; 13 Cout " Enter matrix " 14

{ - mat ans; toans.v[0][0]=ans.v[1][1]=1; + - while(k)///after the second division to be determined * the { * if(k1) $ans=ans*x;Panax Notoginsengx=x*x; -k>>=1; the } + A returnans; the } + - Long LongSolve () $ { $ if(n==0) - return 2; - if(n==1) the returnp; - if(n==2)Wuyi returnp*p-2*Q; the - Mat A; Wua.v[0][0]=p; -a.v[0][1]=-Q; Abouta.v[1][0]=1; $A=pow_mod (a,n-2); - - returna.v[0][1]*p+a.v[0][0]* (p*p-2*q); - } A + int

structMatrix9 {Ten intr,c; OneLL m[3][3]; AMatrixintArrint_c): R (_r), C (_c) {} - }; - voidInit (Matrix m,intAintb) the { -m.m[1][1]=a,m.m[1][2]=-b; -m.m[2][1]=1, m.m[2][2]=0; - } + matrix Multiply (matrix A,matrix b) - { + Matrix M (A.R,B.C); A for(intI=1; ii) { at for(intj=1; jj) { -m.m[i][j]=0; - for(intk=1; kk) -m.m[i][j]+=a.m[i][k]*B.m[k][j]; - } - } in returnm; - } toMatrix Matrix_pow (Matrix M,intN) + { - if(n==0){ them.m[1][1]=m.m[2][2

1, 110501/10035 Primary arithmetic (elementary school arithmetic)Note the output format#include #includestring.h>#include#include#includeusing namespaceStd;typedefLong LongLld;lld A, b;intMain () { while(SCANF ("%lld", a)! =EOF) {scanf ("%lld",b); if(a==0b==0) Break; intCnt=0; inttot=0; while(a!=0|| b!=0) { if(a%Ten+b%Ten+cnt>=Ten) {CNT=1; Tot++; } Else{cnt=0; } A/=Ten; b/=Ten; } if(tot==0) printf ("No"); Elseprintf"%d", tot); if(tot1) printf ("Ca

^nf (x) \rd x}$.6. For integer $a, b$, define $a \equiv b\ (\mod m) $ when and only if $m \mid (A-B) $ (that is, $m $ divisible $a-b$). When a positive integer $m $, what is the solution to a linear equation group? $$\bex \sedd{\ba{rrrrrrl} x+2y-z\equiv1\ (\mod m) \ \ 2x-3y+z\ Equiv4\ (\mod m) \ 4x+y-z\equiv9\ (\mod m) \ea} \eex$$7. Set $\tt$ is real, $n $ is the natural number, ask $$\bex \sex{\ba{cc} e^{-i\tt}2i\sin \tt\\ 0e^{i\tt} \ea}^n. \eex$$8. Set $A, B\in m_n (\BBC) $ ($n $ order complex