Question

After performing the Schur factorization using function Schur in library ‘Matrix’, how do I find the associated unitary matrix in R?

I can do this in MATLAB with the function Schur (documentation here), however, the Schur package in R only provides the triangular in the Schur factorization = $$ U * T * U' $$

Answer 1

Looking at the docs for the “Matrix” package, I noticed that the ‘Schur’ class has a slot for Q, which is the ‘Square orthogonal “Matrix”‘ associated with the decomposition. So you want to do:

Sch.A <- Schur(A);
U <- Sch.A@Q

This is mildly confusing because they quote the decomposition as $A = Q^{\top} T Q$, which is perhaps why you missed it.