```
# NOT RUN {
Schur(Hilbert(9)) # Schur factorization (real eigenvalues)
(A <- Matrix(round(rnorm(5*5, sd = 100)), nrow = 5))
(Sch.A <- Schur(A))
eTA <- eigen(Sch.A@T)
str(SchA <- Schur(A, vectors=FALSE))# no 'T' ==> simple list
stopifnot(all.equal(eTA$values, eigen(A)$values, tolerance = 1e-13),
all.equal(eTA$values,
local({z <- Sch.A@EValues
z[order(Mod(z), decreasing=TRUE)]}), tolerance = 1e-13),
identical(SchA$T, Sch.A@T),
identical(SchA$EValues, Sch.A@EValues))
## For the faint of heart, we provide Schur() also for traditional matrices:
a.m <- function(M) unname(as(M, "matrix"))
a <- a.m(A)
Sch.a <- Schur(a)
stopifnot(identical(Sch.a, list(Q = a.m(Sch.A @ Q),
T = a.m(Sch.A @ T),
EValues = Sch.A@EValues)),
all.equal(a, with(Sch.a, Q %*% T %*% t(Q)))
)
# }
```

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