> A <- matrix(c(3,2,0,3,4,1,0,2,3), 3, 3)
> B <- eigen(A)$vectors %*% diag(1/sqrt(eigen(A)$values)) %*% solve(eigen(A)$vectors)
> eigen(A)$values
[1] 6.3722813 3.0000000 0.6277187
> solve(A)
[,1] [,2] [,3]
[1,] 0.8333333 -0.75 0.5
[2,] -0.5000000 0.75 -0.5
[3,] 0.1666667 -0.25 0.5
> B %*% B
[,1] [,2] [,3]
[1,] 0.8333333 -0.75 0.5
[2,] -0.5000000 0.75 -0.5
[3,] 0.1666667 -0.25 0.5