English
If α is finite and the matrix is block-triangular with respect to blocks labeled by α, the determinant equals the product of the determinants of the diagonal blocks over α.
Русский
Если α конечно и матрица блочно-верхнетреугольна по блочным индексам α, то детерминант равен произведению детерминантов диагональных блоков по α.
LaTeX
$$$\det M = \prod_{k \in \alpha} \det\big(M^{(b)}_k\big)$$$
Lean4
instance charP [DecidableEq n] [Nonempty n] (p : ℕ) [CharP R p] : CharP (Matrix n n R) p where
cast_eq_zero_iff
k := by
simp_rw [← diagonal_natCast, ← diagonal_zero, diagonal_eq_diagonal_iff, CharP.cast_eq_zero_iff R p k, forall_const]
