Past exam of the simulation and statistical programming course of the University of Oxford / 2023 / 3 / c / iii

The Cholesky decomposition gives $\Sigma =L{L}^T$. If $B=L^{-1}$, reversal of factors in a matrix inverse givesHence the required R implementation is

invsigma <- function(sigma) {
  L <- mychol(sigma)
  B <- ltinv(L)
  crossprod(B)
}

Here crossprod(B) computes $B^{T}B$. Using tcrossprod(B) would compute $B{B}^T$, which generally differs from ${\Sigma }^{-1}$. Both helper functions preserve the one-by-one matrix case.