## Numerical check of the push-through identity
Delta=0
for (r in 1:1000){
N=100
n=20
lambda=0.1
X=array(rnorm(N*n),c(N,n))
Delta=Delta+
abs(sum(solve(t(X)%*%X+lambda*diag(n))%*%t(X)-t(X)%*%solve(X%*%t(X)+lambda*diag(N))))
print(Delta )
}
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