from numpy import *
import numpy as np
from numpy import linalg as LA

#Numerically verify these results by drawing a data set from the distribution
#and computing the covariance matrix and eigenvalues.



x = empty((3,3)) #create random matrix 3x3
a = x[:,0]		 #extract column 0
b = x[:,1] 		 #extract colum 1
c = a + b
d = x[:,2] 		
c = d  			#Place "c" in column 2


print x


#Calculate covariance of x: 
covx = np.cov(x)
print covx


#Calculate eigenvalues of x:
w,v = LA.eig(x)
print w;v


#Calculate eigenvalues of covariance of x:
e,f = LA.eig(covx)
print e;f






####################################################
#pts = 1000
#x1 = np.random.random(pts)
#x2 = random.random(pts)
#x3 = x1 + x2
#covx = np.cov(x)

#print covx


#####WORKS
#x = array([[1,0,1],[0,1,1],[1,1,2]])
#Calculate eigenvalues:
#w,v =  LA.eig(x)
#print w;v

#Calculate the Covariance:
#print np.cov(w,v)