eigenvector - Eigen Values and Eigen Vectors Matlab -


i have matrix a

a = [ 124.6,95.3,42.7 ; 95.3,55.33,2.74 ; 42.7,2.74,33.33 ]

the eigenvalues , vectors:

[v,d] = eig(a)

how show eigenvalues mutually perpendicular? i've tried if dot product of eigenvalues zero, demonstrates mutually perpendicular, how compute in matlab? tried following code

transpose(diag(d)) * diag(d)  %gives 4.1523e+04

also, how can verify definition of eigenvalues , vector holds:

a e_i - l_i e_i = 0

the above equation: equal 1 3. real, symmetric matrix eigenvales positive numbers , eigenvectors basis matrix

i tried following code, doesn't seem give me 0. ideas?

a*v(1) - d(1)*v(1)

to show orthogonality

>> v'*v-eye(size(v))  ans =     1.0e-15 *      0.2220    0.1110    0.2498     0.1110   -0.4441    0.1388     0.2498    0.1388    0.4441

to show definition of eigendecomposition satisfied,

>> a*v - v*d  ans =     1.0e-13 *      0.4086    0.0400    0.8527     0.3908    0.0355    0.5684     0.1954    0.0355         0

the results won't zero, because digital computers don't exact math, can see they're pretty close.


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