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if not using

EigenvectorSol := simplify(solve({seq(seq((NewMatrix3 . NewInput3(1..-1,i))[j]=(v[i]* NewInput3(1..-1,i))[j], j=1..3), i=1..3)}, {seq(x||i, i=1..9)}));

and if want to see clearly the steps about how to solve for eignvector, how to do?

because i use solve, it has error

InputMatrix3 := Matrix([[31.25,30.8,30.5],[30.8,30.5,0],[30.5,0,0]]);

NewInput3 := MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3);

FirstEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[1]; # find back eigenvalue from eigenvector

SecondEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[2]; # find back eigenvalue from eigenvector

ThirdEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[3]; # find back eigenvalue from eigenvector

v:=[ FirstEigenValue, SecondEigenValue, ThirdEigenValue];

NewMatrix3 := Matrix([[x1,x2,x3], [x4,x5,x6], [x7,x8,x9]]);

EigenvectorSol := simplify(solve({seq(seq((NewMatrix3 . NewInput3(1..-1,i))[j]=(v[i]* NewInput3(1..-1,i))[j], j=1..3), i=1..3)}, {seq(x||i, i=1..9)}));

EigenvectorT := Matrix([[rhs(EigenvectorSol[1]), rhs(EigenvectorSol[2]), rhs(EigenvectorSol[3])],[ rhs(EigenvectorSol[4]), rhs(EigenvectorSol[5]), rhs(EigenvectorSol[6])],[ rhs(EigenvectorSol[7]), rhs(EigenvectorSol[8]), rhs(EigenvectorSol[9])]]);

Old_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3));

 

sys1:=MatrixMatrixMultiply(NewInput3-Matrix([[FirstEigenValue, 0, 0], [0, FirstEigenValue, 0], [0, 0, FirstEigenValue]]),Matrix([[x],[y],[z]]));

sys1a := NewInput3-Matrix([[FirstEigenValue, 0, 0], [0, FirstEigenValue, 0], [0, 0, FirstEigenValue]]);

 

fsolve({sys1[1][1]=0,sys1[2][1]=0,sys1[3][1]=0}, {x,y,z});

solve([sys1[1][1]=0,sys1[2][1]=0,sys1[3][1]=0], [x,y,z]);

solve([sys1[1]=0,sys1[2]=0,sys1[3]=0], [x,y,z]);

> solve([sys1[1] = 0, sys1[2] = 0, sys1[3] = 0], [x, y, z]);

Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({set, list})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received [(Vector[row](1, {(1) = HFloat(2571.1332294000003)*x+HFloat(1901.9)*y+HFloat(953.125)*z})) = 0, (Vector[row](1, {(1) = HFloat(1901.9)*x+HFloat(1594.5707294000001)*y+HFloat(939.4)*z})) = 0, (Vector[row](1, {(1) = HFloat(953.125)*x+HFloat(939.4)*y+HFloat(645.9307294)*z})) = 0]

 

 

v1 := <sys1a[1,1] | sys1a[1,2] | sys1a[1,3]>;

v2 := <sys1a[2,1] | sys1a[2,2] | sys1a[2,3]>;

v3 := <sys1a[3,1] | sys1a[3,2] | sys1a[3,3]>;

 

v1 := <sys1a[1,1] | sys1a[2,1] | sys1a[3,1]>;

v2 := <sys1a[1,2] | sys1a[2,2] | sys1a[3,2]>;

v3 := <sys1a[1,3] | sys1a[2,3] | sys1a[3,3]>;

eigenvector1 := Basis([v1, v2, v2]);

eliminate({sys1[1][1]=0,sys1[2][1]=0,sys1[3][1]=0},{x,y,z});

eliminate({sys1[1][1]=0,sys1[1][2]=0,sys1[1][3]=0},{x,y,z});

 

sys1:=MatrixMatrixMultiply(NewInput3-Matrix([[SecondEigenValue, 0, 0], [0, SecondEigenValue, 0], [0, 0, SecondEigenValue]]),Matrix([[x],[y],[z]]));

solve([sys1[1][1]=0,sys1[2][1]=0,sys1[3][1]=0], [x,y,z]);

sys1:=MatrixMatrixMultiply(NewInput3-Matrix([[ThirdEigenValue, 0, 0], [0, ThirdEigenValue, 0], [0, 0, ThirdEigenValue]]),Matrix([[x],[y],[z]]));

solve([sys1[1][1]=0,sys1[2][1]=0,sys1[3][1]=0], [x,y,z]);

 

https://drive.google.com/file/d/0B2D69u2pweEvUDJIeGlOVjFvNWc/edit?usp=sharing
https://drive.google.com/file/d/0B2D69u2pweEvV1BiRXhULTNPcWM/edit?usp=sharing
https://drive.google.com/file/d/0B2D69u2pweEvdXNrRlNadldXS0U/edit?usp=sharing

i find that maple 15 values are the same as extreme optimization library however, the sign are different

is it maple 15 accuracy correct or extreme library correct?

https://drive.google.com/file/d/0B2D69u2pweEvT01pazBxOEk1bWc/edit?usp=sharing

i worry for my research whether based on correct accuracy.

 

it can run without error in maple 15, however, the eigenvector values are wrong in maple 15 different from eigenvector function's result

then i test it in maple 12, it got error when run with following input

Warning, solutions may have been lost
Error, invalid input: simplify uses a 1st argument, s, which is missing
> InputMatrix3;
                           [[30.15,29.95,29.95],[29.95,29.95,0],[29.95,0,0]]

NewInput3 := MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3);
FirstEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[1]; # find back eigenvalue from eigenvector
SecondEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[2]; # find back eigenvalue from eigenvector
ThirdEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[3]; # find back eigenvalue from eigenvector
v:=[ FirstEigenValue, SecondEigenValue, ThirdEigenValue];
NewMatrix3 := Matrix([[x1,x2,x3], [x4,x5,x6], [x7,x8,x9]]);
EigenvectorSol := simplify(solve({seq(seq((NewMatrix3 . NewInput3(1..-1,i))[j]=(v[i]* NewInput3(1..-1,i))[j], j=1..3), i=1..3)}, {seq(x||i, i=1..9)}));
EigenvectorT := Matrix([[rhs(EigenvectorSol[1]), rhs(EigenvectorSol[2]), rhs(EigenvectorSol[3])],[ rhs(EigenvectorSol[4]), rhs(EigenvectorSol[5]), rhs(EigenvectorSol[6])],[ rhs(EigenvectorSol[7]), rhs(EigenvectorSol[8]), rhs(EigenvectorSol[9])]]);
Old_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3));

with(LinearAlgebra):
t:=1;
NewMatrix3 := Matrix([[test10, close3(t) , close3(t+1)],
[close3(t) , close3(t+1) ,0],
[close3(t+1) , 0,0]]);

Matrix(3, 3, {(1, 1) = test10, (1, 2) = 5.59, (1, 3) = 5.74, (2, 1) = 5.59, (2, 2) = 5.74, (2, 3) = 0, (3, 1) = 5.74, (3, 2) = 0, (3, 3) = 0})

NewEigenMatrix := Eigenvalues(NewMatrix3);
solve([MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[1][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[1][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[2][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[2][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[3][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[3][1]]
, [x,y,z]);

expect to calculate a eigenvector in terms of variable test10

close3 are decimal value

> NewMatrix3 := Matrix([[test10, close3(t), close3(t+1), close3(t+2), close3(t+3), close3(t+4)], [close3(t), close3(t+1), close3(t+2), close3(t+3), close3(t+4), close3(t+5)], [close3(t+1), close3(t+2), close3(t+3), close3(t+4), close3(t+5), 0], [close3(t+2), close3(t+3), close3(t+4), close3(t+5), 0, 0], [close3(t+3), close3(t+4), close3(t+5), 0, 0, 0], [close3(t+4), close3(t+5), 0, 0, 0, 0], [close3(t+5), 0, 0, 0, 0, 0]]); New_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(NewMatrix3), NewMatrix3));


Error, (in LA_Main:-Eigenvectors) cannot determine if this expression is true or false: abs(149.8198+5.59*Re(test10))+27.38*abs(Im(test10))+abs(118.8174+5.74*Re(test10))+abs(90.3603+5.49*Re(test10))+abs(61.9327+5.19*Re(test10))+abs(31.0804+5.37*Re(test10)) < (1/10)*abs(149.8198+5.59*Re(test10))+2.738000000*abs(Im(test10))+(1/10)*abs(118.8174+5.74*Re(test10))+(1/10)*abs(90.3603+5.49*Re(test10))+(1/10)*abs(61.9327+5.19*Re(test10))+(1/10)*abs(31.0804+5.37*Re(test10))

 

I was working with the computation of the eigenvectors of a 3X3 symmetric matrix with algebraic entries and Maple 17 doesn´t give me an answer after a long time, even with CUDA activated. You can see this by the commands below:

 


Hey,

I have currently encountered a problem that I am not sure if is a mathematical problem or a problem with Maple itself. I want to find the eigenvalues and eigenvectors of the following matrix:

[[2.460*10^9*sin(theta)^2+8.970*10^6*cos(theta)^2, 0, 2.449*10^9*sin(theta)*cos(theta)], [0,8.450*10^6*sin(theta)^2+8.970*10^6*cos(theta)^2,0],[2.449*10^9*sin(theta)*cos(theta),8.970*10^6*sin(theta)^2+2.530*10^9*cos(theta)^2]]

Maple is able to conjure...

mech_problem.mw

Hi

I solve a mechanical exercise but i had a problem.

I know M (mass) and S (stifness) matrices (6x6).

I want to solve the (λ2M+S)v=0  eigenvalue problem, where λ are the eigenvalues and

Hi, I have a matrix D which is a 33x33 matrix. I find the eigenvector using "Eigenvectors(D)". It gives me the eigenvalue together with the eigenvector. Then, i want to multiply the eignevector with another 33x33 matrix. How can I get the eigenvector without the eigenvalues attached to it? please advice.

Many thanks.

[A]+[B] N+[C] N^(2)+[D] N^(3)+...N^(8)

[A],[B],[C],[D],... is known 8*8 matrix ;

how to find Eigenvalues and Eigenvectors and N?

eig([A],[B],[C],[D],...) ?!?!?

Hello Everybody.

Im new to Maple, so i have a couple of questions. In the last few days I have learned the basic of Maple, and now i would like to solve an differential equation.

The Math question is:

Enter the solution of differential equation:

http://www.studieportalen.dk/forums/ShowFile.aspx?id=1122047

In the link i have put in the informations from the math question.

Help!

I've used Eigenvectors to solve for eigenvalues & eigenvectors.  Eigenvalues works, no problem.

The eigenvectors are not normalized to unit magnitude (how would I do that for all eigenvectors?) and the usual matrix multiplication of the eigenmatrix by its transpose should give the identity matrix--and somehow it does not. 

Can someone point out the flaw in my thinking?  The file is attached.

 

Thanks for you insight! 

I am dissapointed. I recently upgraded to Maple 15 and I bought a license for the NAG libraries thinking that I could use NAG mark 8 chapter F12 to solve my Eigenvalue problem with large sparse matrix, in reality, there seems to be no implementation of these NAG routines in Maple. is there a way to get around this problem? I know I can also connect to MATLAB to take advantage of the integrated sparse handling but I want to avoid buying another piece of software(you know we scientist aren't millionaries).

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