= Solution
The <Cholesky decomposition> gives $\Sigma=LL^T$. If $B=L^{-1}$, reversal of factors in a <matrix inverse> gives
$$
\boxed{\Sigma^{-1}=(L^T)^{-1}L^{-1}=B^TB.}
$$
Hence the required <R (programming language)> implementation is
``
invsigma <- function(sigma) {
L <- mychol(sigma)
B <- ltinv(L)
crossprod(B)
}
``
Here `crossprod(B)` computes $B^TB$. Using `tcrossprod(B)` would compute $BB^T$, which generally differs from $\Sigma^{-1}$. Both helper functions preserve the one-by-one <matrix> case.
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