In [1]:
# rm(list=ls()) 
options(OutDec = ",")
#==============================================================================
# Exemplo 
#==============================================================================
SIGMA <- matrix(c(19,30,2,12,30,57,5,23,2,5,38,47,12,23,47,68),4,4,T)
L     <- matrix(c(4,1,7,2,-1,6,1,8),4,2,T)
PSI   <- diag(c(2,4,1,3))

print("==== SIGMA ====")
print(SIGMA)
print("==== L ====")
print(L)
print("==== PSI ====")
print(PSI)
print("==== Verificando os valores ====")
print(L%*%t(L)+PSI)             
print("==== Todos iguais a zero ====")
print(SIGMA - (L%*%t(L) + PSI))

[1] "==== SIGMA ===="
     [,1] [,2] [,3] [,4]
[1,]   19   30    2   12
[2,]   30   57    5   23
[3,]    2    5   38   47
[4,]   12   23   47   68
[1] "==== L ===="
     [,1] [,2]
[1,]    4    1
[2,]    7    2
[3,]   -1    6
[4,]    1    8
[1] "==== PSI ===="
     [,1] [,2] [,3] [,4]
[1,]    2    0    0    0
[2,]    0    4    0    0
[3,]    0    0    1    0
[4,]    0    0    0    3
[1] "==== Verificando os valores ===="
     [,1] [,2] [,3] [,4]
[1,]   19   30    2   12
[2,]   30   57    5   23
[3,]    2    5   38   47
[4,]   12   23   47   68
[1] "==== Todos iguais a zero ===="
     [,1] [,2] [,3] [,4]
[1,]    0    0    0    0
[2,]    0    0    0    0
[3,]    0    0    0    0
[4,]    0    0    0    0
In [2]:
#==============================================================================
# Comunalidades 
#==============================================================================
sum2 <- function(x){return(sum(x^2))}
h    <- apply(L,1,"sum2")
print(h)

[1] 17 53 37 65