## Eigenvalues. Mechanical problem...

I solve a mechanical exercise but i had a problem.

I know M (mass) and K (stifness) matrices (4x4).

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

How can i solve this problem.  I tried with the Eigenvectors() command but it didn't give the right solution.

The Eigenvalues are okay, but the eigenvectors not

K := Matrix([[4*10^7,-1.50*10^7,2*10^7,0],[-1.50*10^7,1.50*10^7,0,1.50*10^7],[2*10^7,0,8*10^7,2*10^7],[0,1.50*10^7,2*10^7,4*10^7]]);

M:=Matrix([[121.90,99.048,-91.429,0],[99.048,594.29,0,-99.048],[-91.429,0,243.81,-91.429],[0,-99.048,-91.429,121.90]]);

w1,w2:=Eigenvectors(K,M);

Acoording with the book the right eigenvectors(shape mode) are:

[0.013 991,  0.034 233,  0.073 683,  0.090 573]
[0.035 637, 0, -0.032 213, 0]
[0 ,-0.034 233, 0, 0.090 573]
[-0.013 991, 0.034 233, -0.073 683, 0.090 573]

Thank you

## how can i sorts the vector in Eigenvectors...

hi.i cant write english very well. excuse me

i solve the Eigenvectors of two matrix. first i want to delete complex numbers in solve. and then sort the little vector in first matrix of vector. as this picture

1.mw

code

k__1 := (12*2)*10^6/3^3; k__2 := k__1; k__3 := (3*1.5)*10^6/3^3; k__4 := (12*1.5)*10^6/3^3; k__5 := 12*10^6/3^3; m__1 := 8000; m__2 := 7000; m__3 := 6000; m__4 := 5000; m__5 := 10000; K := Matrix(5, 5, [[k__1+k__2, -k__2, 0, 0, 0], [-k__2, k__2+k__3, -k__3, 0, 0], [0, -k__3, k__3+k__4, -k__4, 0], [0, 0, -k__4, k__4+k__5, -k__5], [0, 0, 0, -k__5, k__5]]); M := Matrix(5, 5, [[m__1, 0, 0, 0, 0], [0, m__2, 0, 0, 0], [0, 0, m__3, 0, 0], [0, 0, 0, m__4, 0], [0, 0, 0, 0, m__5]])

## I want to write this function withÂ Â "for"...

hello. i want to write this function with  "for"loop. but i don't know
1.mw

## Eigenvalues , eigenvectors and Fundamental Matrix...

How to write a code find fundamental matrix of the following Matrix?

```restart; with(LinearAlgebra): A:=Matrix([[0, 1, 0, 0], [-a, 0, b, 0], [0, 0, 0, 1], [c, 0, -d, 0]]);eigenvectors(A);
```

where a,b,c,d∈IR.

I want to find eigenvalues and eigenvectors and then want to calculate e^( λ i)*ri  where λi's are eigenvalues, ri's are eigenvectors of A for i=1,2,3,4  respectively.

Then, I want to calculate Wronskian of the matrix which consists of vectors e^(λi)*ri in the columns. Could you help me?

## linearalgebra,equation ...

hello . how can i get 7 given parameters(b1,a1,b1,a2,b2,.....) in this equation with maple. thanks

1.mw

## How do you recommend to calculate the square root ...

How do you recommend to calculate the square root of big Matrices (e.g, 300*300) with Maple??

My machine couldnt calculate the square root of Matrices (9*9) as you see below:

 >
 >
 >
 >
 (1)
 >
 >
 >
 >
 >
 >

## How ask Maple to arrange linear equations in Matri...

I have many linear equations as below(f,g,h,...,p, are linear of S,T,..,W):

y1=f(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

y2=g(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

y3=h(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

.

.

.

yn=p(S[i,j],T[i,j],U[i,j],V[i,j],W[i,j]);

Where (i,j)=(0,0),...,(I,J)

How ask Maple to write them in Matrix form as below:

AX=0

Where X is: X=Transpose{S[0,0],S[0,1],S[0,J],...,S[1,0],S[1,1],...,S[1,J],...,S[I,0],S[I,1],...,S[I,J],

T[0,0],T[0,1],T[0,J],...,T[1,0],T[1,1],...,T[1,J],...,T[I,0],T[I,1],...,T[I,J],...,W[I,J]}

## differences between numeric and symbolic eigendec...

Dear Maple experts,

I am struggling with a difference between the symbolic and numerical solution of an eigendecomposition of a symmetric positive definite matrix. Numerically the solution seems correct, but the symbolic solution puzzles me. In the symbolic solution the reconstructed matrix is different from the original matrix (although the difference between the original and the reconstructed matrix seems to be related to an unknown scalar multiplier.

restart;
with(LinearAlgebra);
Lambda := Matrix(5, 1, symbol = lambda);
Theta := Matrix(5, 5, shape = diagonal, symbol = theta);
#Ω is the matrix that will be diagonalized.
Omega := MatrixPower(Theta, -1/2) . Lambda . Lambda^%T . MatrixPower(Theta, -1/2);
#Ω is symmetric and in practice always positive definite, but I do not know how to specify the assumption of positivess definiteness in Maple
IsMatrixShape(Omega, symmetric);

# the matrix Omega is very simple and Maple finds a symbolic solution
E, V := Eigenvectors(Omega);

# this will not return the original matrix

simplify(V . DiagonalMatrix(E) . V^%T)

# check this numerically with the following values.

lambda[1, 1] := .9;lambda[2, 1] := .8;lambda[3, 1] := .7;lambda[4, 1] := .85;lambda[5, 1] := .7;
theta[1, 1] := .25;theta[2, 2] := .21;theta[3, 3] := .20;theta[4, 4] := .15;theta[5, 5] := .35;

The dotproduct is not always zero, although I thought that the eigenvectors should be orthogonal.

I know eigenvector solutions may be different because of scalar multiples, but here I am not able to understand the differences between the numerical and symbolic solution.

I probably missed something, but I spend the whole saturday trying to solve this problem, but I can not find it.

I attached both files.

Harry

eigendecomposition_numeric.mw

eigendecomposition_symbolic.mw

## LinearSolve Results...

Hi Maple Community,

I just got my Maple licence and currently I'm going thorugh some basic tutorials in which I've encountered a problem I can't seem to fix:

I'm trying to use the 'LinearSolve' solver as it is shown in the examples on the Maplesoft.com support page:

But I can't seem to get Maple to display a result like it is shown in the picture above.