Theorems · Theorem · linear algebra

Matrix.BlockTriangular.toBlock_inverse_mul_toBlock_eq_one

∀ {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 : LinearOrder α] [Invertible M],
  M.BlockTriangular b →
    ∀ (k : α), ((M⁻¹.toBlock (fun i => b i < k) fun i => b i < k) * M.toBlock (fun i => b i < k) fun i => b i < k) = 1

Defined in

Mathlib.LinearAlgebra.Matrix.Block

Cited by

1 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingDecidableEqFintypeLinearOrderInvertible