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how can i calculate eigenvalue and eigenvectors for a big Matrix?

example Matrix 12*12.


thank you

Hi fellow Maple users,

I'm trying to solve an eigenvalue problem of Ax=wx, where A is a 6 by 6 Hermitian matrix with two parameters x and y. I want to solve it for w and then plot3d it with x and y as unknowns. The way I have been doing is first find the characteristic equation Determinant(A-wI)=0 and then solve it for w, and then plot3d the solutions within a range for x and y. My problem is sometimes solve(Determinant(A-wI)=0,w) would give me the 6 solutions expressed in x and y, but sometimes when the numbers in A are changed it will only give me a Rootof solution with which I cannot plot. I'm wondering if there is a better way to do this. I'm actually not very interested in the symbolic solution of w expressed in x and y, just the plot, so if there is a numerical alternative it's good too.

Thank you in advance!


Gerschgorin := proc (A::Matrix) local Delta, m, n, AA, R, C, i, c, eig, P, Plt; Delta := proc (i, j) if i = j then 0 else 1 end if end proc; m, n := LinearAlgebra[Dimension](A); AA := Matrix(m, n, proc (i, j) options operator, arrow; Delta(i, j)*abs(A[i, j]) end proc); R := evalm(`&*`(AA, Vector(m, 1))); C := {seq(('plottools[circle]')([Re(A[i, i]), Im(A[i, i])], R[i], color = violet), i = 1 .. m)}; c := {seq(('plottools[point]')([Re(A[i, i]), Im(A[i, i])], color = blue, symbol = diamond), i = 1 .. m)}; eig := evalf(LinearAlgebra[Eigenvalues](A)); P := {seq(('plottools[point]')([Re(eig[i]), Im(eig[i])], color = red, symbol = box), i = 1 .. m)}; Plt := `union`(`union`(C, c), P); plots[display](eval(Plt), scaling = constrained) end proc


A := Matrix([[5, 8, 4, -3], [8, -9, 7, 5], [0, 4, 4, 2], [5, -5, 9, -9]]); evalf(LinearAlgebra[Eigenvalues](A), 3); Gerschgorin(A)



F := Matrix([[2, -1/2, -1/3, 0], [0, 6, 1, 0], [1/3, -1/3, 5, 1/3], [-1/2, 1/4, -1/4, 4]]); evalf(LinearAlgebra[Eigenvalues](F)); Gerschgorin(F)

Could you print A & F ?





I have the following characteristic equation by use of maple. How do I find a condition on x, that will return real eigenvalues and complex eigenvalues?




If I have the following system of first order diff eq's:



then can I consider the coefficient matrix A=<<2,-3>,<3,-2>> and compute the eigenvalues of A and infer as follows:

if the eigenvalues are of the same sign- eq point is a node

if they are of opposite signs- eq point is a saddle

if they are pure imaginary- eq point is a center

if they are complex conjugates- eq. point is a spiral

I've been given these conditions but my text says for a linear system of the form x'=Ax, the eigenvalues of A can be used to identify the nature of the eq. point. I am confused as to whether this applies to the given system as well; I have obtained 5 different trajectories and drawn the phase diagram for the system


  Is there any benchmark of the performance of maple on windows 7 64 bit vs linux, especially in solving generalized eigenvalue problem?


Thank you very much

I calculate eigenvalues and  eigenvectors of a floating-point square matrix M with the command Eigenvectors(M, output = 'list').  How can I estimate errors of my results?

So, newb question here. I've done my best to debug this line of code, but to no avail. For some reason this function is NOT getting solved correcting for the zeros:

cos(L*x) - x*sin(L*x)


This is not an extremely complex equation either, so I'm at a loss for why my while loop continues to sit there forever. I've got it set to find N number of zeros, but it'll just keep going forever never finding any zeros. I've tried mixing up the start point, and even changed the range which it's searching for them, but nothing seems to get me any closer. Please help!


> restart; with(plots);
> a := 0; b := 1/2; N := 5; w := 1; L := b-a;

Eigenvalue equation
> w := cos(L*x)-sin(L*x)*x;
> plot(w, x = 0 .. 50);

> lam := array(0 .. N+1);

> nn := 0; kk := 5; while nn < N do zz := fsolve(w(x) = 0, x = kk .. kk+1); if type(zz, float) then printf("lam(%d)=%f\n", nn, zz); lam[nn] := zz; nn := nn+1 end if; kk := kk+1 end do



i want to find the eigenvalues of this system of two equations with two unknowns:

2.097*k = .9525000000*k^.35-2.2225*b/k^.65+.2 and

(2.097-2.0955/k^.67)*b = -.2

How i can do this in Maple?

Any help will be appreciated

Eigenvectors(A, C) can be used to solve the eigenvalue problem:
A . x = lambda . C . x

if a new term " lambda^2 . D . x " is added to the right hand side, where D is a new matrix, is there a simple way to solve the new eigenvalue problem:

A . x = lambda . C . x + lambda^2 . D . x

Thank you!


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

Hello every one,

I want to plot two parameters against each other from a system of ode.

The system is





N:=10: M:=0.1:



I was trying to find the generalized eigenvalues for the (3x3) matrix pair (P,G) defined below. (I have left everything in symbols with beta and kappa both of which are strictly positive real numbers). For some reason the command Eigenvalues(P,G) is only returning 2 generalized eigenvalues. Any ideas why it doesn't return 3?




I am looking for a numerical scheme which can easly handle such type of problem.

I already had the analytical results of this problem, now I want to know how to treat this problem numerically.

Any idea, then please let me know.


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