Theorems · Theorem · linear algebra

Matrix.BlockTriangular.det

∀ {α : Type u_1} {m : Type u_3} {R : Type v} {M : Matrix m m R} {b : m → α} [inst : CommRing R] [inst_1 : DecidableEq m]
  [inst_2 : Fintype m] [inst_3 : DecidableEq α] [inst_4 : LinearOrder α],
  M.BlockTriangular b → M.det = ∏ a ∈ Finset.image b Finset.univ, (M.toSquareBlock b a).det

Defined in

Mathlib.LinearAlgebra.Matrix.Block

Cited by

3 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingDecidableEqFintypeDecidableEqLinearOrder