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Final Review Am s 211 Sol
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Clif Pottberg Arron Phillips MATLAB Project 4 function [m] = mult(A,ev1,ev2) lambda=eig(A); [i,j] = size(lambda); m1 = 0; m2 = 0; row = 1; tol = 10^(-7); while row<=i difference1 = lambda(row,1) - ev1; difference2 = lambda(row,1) - ev2; if abs(difference1) < tol m1 = m1+1; elseif abs(difference2) < tol m2 = m2+1; end row = row+1; end disp('multiplicity of eigenvalue 1:') disp(m1) disp('multiplicity of eigenmulvalue 2:') disp(m2) end This function utilizes the built in matlab function eig(A) to output the eigenvalues of as a column vector, and then compares input eigenvalues with the eigenvalues of the input matrix to test their respective multiplicities.
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function [d] = disteig(A) lambda=eig(A); [i,j] = size(lambda); L=logical(ones(i)); rowcurrent = 1; tol = 10^(-7); while rowcurrent<=i ev=lambda(rowcurrent,1); for rowcompare=rowcurrent+1:i if abs(ev-lambda(rowcompare,1))
This function finds the distinct eigenvalues of A and outputs them in a column vector It accomplishes this by utilizing the skeletal structure of the last program in conjunction with a logical array of ones. The while loop with contained nested for loop compares the current eigenvalue with other eigenvalues, but not itself. If they You're Reading a Preview are equal to another eigenvalue within the specified tolerance, their corresponding entry in the logical array is set Unlock equalfull toaccess zero.with a free trial. Thus the distinct eigenvalues are pulled from the output column vector Download Free corresponding to the logical array entriesWith which areTrial still one.
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Final Review Am s 211 Sol
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function [P] = eigbasis(A) lambda = eig(A); [i,j] = size(lambda); P = zeros(i,i); counter1=1; counter2=0; tol=10^(-7); while counter1<=i ev = lambda(counter1,1); B = newnullbase(A-eye(i,i)*ev); for counter2=0:i-1 if abs(B(:,1)-P(:,i))tol; end end P(:,counter1) = B(:,1); counter1=counter1+1; counter2=1; end if det(P)==0 error('The input matrix is not diagnalizable. P not invertible.') end You're Reading a Preview end Unlock full access with a free trial.
This program outputs a matrix whose columns are the eigenspace of the input matrix. A relatively similar structure to the other two, except for this program a simpl Download With Free Trial of entries rather than matrix of zeros has been utilized for direct replacement representation by a logical array. In the while loop with nested for loop, the newnullbase program is utilized as a shortcut method to solving the homogeneous equation [A-Lambda*I]*X=0 and then looping through all eigenvalues given for the input matrix by eig(A) to find their Read Free Foron 30 Days Sign up to vote this title corresponding eigenvectors. The nested for loop within the while loop simply compares the current eigenvector with the previously inputtedeigenvectors and Not useful Useful Cancel anytime. assures they are not equal, with respect to the specified tolerance. This step Special offer for students: Onlythat $4.99/month. assures linear independence of the columns of the eigenvector matrix P. If the
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>> A=[2 2 3; 0 3 -1; 0 2 0] Sheet Music
A= 2 0 0
2 3 2
3 -1 0
>> mult(A,0,2) multiplicity of eigenvalue 1: 0 multiplicity of eigenmulvalue 2: 2 >> disteig(A) distinct eigenvalues of input matrix: ans = 2 1 >> eigbasis(A) ??? Error using ==> eigbasis at 38 You're The input matrix is not diagnalizable. P notReading invertible.a Preview Unlock full access with a free trial.
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>> B=[3 2; -2 3] Sheet Music
B= 3 -2
2 3
>> mult(B,0,2) multiplicity of eigenvalue 1: 0 multiplicity of eigenmulvalue 2: 0 >> disteig(B) distinct eigenvalues of input matrix: ans = 3.0000 + 2.0000i 3.0000 - 2.0000i >> eigbasis(B)
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ans = 0 - 1.0000i 1.0
0 + 1.0000i 1.0000
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>> C = magic(6) Sheet Music
C= 35 1 3 32 31 9 8 28 30 5 4 36
6 26 19 24 7 21 23 25 2 22 27 20 33 17 10 15 34 12 14 16 29 13 18 11
>> mult(C,0,2) multiplicity of eigenvalue 1: 1 multiplicity of eigenmulvalue 2: 0 >> disteig(C) distinct eigenvalues of input matrix: ans = 111.0000 27.0000 -27.0000 9.7980 -0.0000 -9.7980
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>> eigbasis(C) ans = -1.0000 -1.0000 8.8298 2.0000 -0.6747 Master your1.0000 semester with Scribd 1.0000 2.0000 -1.0000 24.0853 2.0000 -0.6985 Read Free Foron 30this Days Sign up to vote title 1.0000 -1.0000 -1.0000 -15.2482 -1.0000 0.1223 & The New 1.0000 York 1.0000 Times 1.0000 25.0780 -2.0000 0.2031 Useful Not useful 1.0000 -2.0000 1.0000 -43.7449 -2.0000 0.0478 Special offer for students: Only $4.99/month. 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
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>> D = reshape(1:25,5,5) Sheet Music
D= 1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25
>> mult(D,0,2) multiplicity of eigenvalue 1: 3 multiplicity of eigenmulvalue 2: 0 >> disteig(D) distinct eigenvalues of input matrix: ans = 68.6421 -3.6421 0.0000
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>> eigbasis(D) ??? Error using ==> eigbasis at 38 Unlock full access with a free trial. The input matrix is not diagonalizable. Eigenvectors are not linearly independent.
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>> E = rand(4,4) Sheet Music
E= 0.2769 0.0462 0.0971 0.8235
0.6948 0.3171 0.9502 0.0344
0.4387 0.3816 0.7655 0.7952
0.1869 0.4898 0.4456 0.6463
>> mult(E,0,2) multiplicity of eigenvalue 1: 0 multiplicity of eigenmulvalue 2: 0 >> disteig(E) distinct eigenvalues of input matrix: ans = 1.8891 -0.0021 + 0.4886i -0.0021 - 0.4886i 0.1210 >> eigbasis(E)
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ans = Columns 1 through 3 0.6026 0.5513 0.9150 1.0000
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-0.2663 + 0.4144i -0.2663 - 0.4144i -0.1159 - 0.4839i -0.1159 + 0.4839i -0.5346 + 0.2063i -0.5346 - 0.2063i 1.0000 1.0000
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>> F = diag([1 0 0 0],1)+diag([2 2 2 4 4]) Sheet Music
F= 2 0 0 0 0
1 2 0 0 0
0 0 2 0 0
0 0 0 4 0
0 0 0 0 4
>> mult(F,0,2) multiplicity of eigenvalue 1: 0 multiplicity of eigenmulvalue 2: 3 >> disteig(F) distinct eigenvalues of input matrix: ans = 2 4
You're Reading a Preview >> eigbasis(F) ??? Error using ==> eigbasis at 38 Unlock fullinvertible. access with a free trial. The input matrix is not diagnalizable. P not Download With Free Trial
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