In [1]:

    

require(matrixcalc)


    

    




Loading required package: matrixcalc

In [2]:

    

Sigm <- matrix(c(283, 215, 277, 208, 215, 213, 217, 153, 277, 217, 336, 236, 208, 153, 236, 194), nrow=4)
Sigm


    

    
Out[2]:






	
283
215
277
208
	
215
213
217
153
	
277
217
336
236
	
208
153
236
194

In [3]:

    

tr <- matrix.trace(Sigm)
tr


    

    
Out[3]:




1026

In [4]:

    

eigen_val_vec <- eigen(Sigm, symmetric=TRUE)
vect <- eigen_val_vec$vectors
vect


    

    
Out[4]:






	
-0.5357934
 0.1912818
 0.7050231
-0.4234138
	
-0.4320336
 0.7687151
-0.3416228
 0.3251431
	
-0.5834990
-0.4125759
-0.5727115
-0.4016360
	
-0.4310468
-0.4497438
 0.2413252
 0.7441044

In [5]:

    

v1 <- vect[,1]
v1


    

    
Out[5]:





	
-0.53579338191969
	
-0.432033597170025
	
-0.583499015959617
	
-0.431046773774668

In [6]:

    

norm(as.matrix(v1), "f")


    

    
Out[6]:




1

In [7]:

    

lambda1 <- eigen_val_vec$values[1]
lambda1


    

    
Out[7]:




925.363626300051

In [8]:

    

lambda1/tr


    

    
Out[8]:




0.901913865789523