eigenvalue
[1] 2.5897826 1.5156007 1.8060659 0.9620865
eigenvector
[1][2]
[1] 0.2364211 0.178445138
[2] -0.1055865 -0.3364896
There should be 7 eigen values and eigenvector but I remove it to make it easier, I want to know how to calculate it
Can someone help me how to calculate norm for eigenvector and prove that eigenvectors are pairwise orthogonal?
For the norm of eigenvectors, I tried to calculate the sum of squared of eigenvector [1], for example the result is 0.70 (not actual result). After that I square root the sum of squared, which is squared root of 0.70 = 0.836
after getting the result, what should I do?
Thank you for your help
Norm in R shows how to calculate the norm of a vector in R. You can use that for each of your eigenvectors.
I found that with a Google search for r norm of vector
Norm[{3,4}] will calculate the norm of that vector in Mathematica.
If you want to calculate the norm of a vector by hand then it is as you describe, the square root of the sum of the squared elements of the vector. Thus the norm of the vector 3,4 is sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5
Dot product in R shows how to calculate the dot product of two vectors in R. If two vectors are orthogonal then the dot product should equal zero and not otherwise. You can use that for each pair of your eigenvectors.
I found that with a Google search for r dot product of vectors
Dot[{1,0},{0,5}] will calculate the dot product of those two vectors in Mathematica.
If you want to calculate the dot product of two vectors by hand then it is either a.b=norm(a)*norm(b)*Cos(angle between the two vectors) or it is a1*b1+a2*b2 where your two vectors are a=a1,a2 and b=b1,b2.
If you wanted to edit your post to show your complete square matrix of data then I would calculate the eigenvectors and eigenvalues and norms and dot products in Mathematica and edit this to show the result and you could compare my results with yours. Or if you can show where I can scrape your matrix off the web without me needing to sign in/sign up/etc then I could use that.