Theorems · Theorem · linear algebra

Matrix.toBlock_inverse_eq_zero

∀ {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 => k ≤ b i) fun i => b i < k) = 0

A lower-left subblock of the inverse of a block-triangular matrix is zero. This is a first step towards BlockTriangular.inv_toBlock below.

Defined in

Mathlib.LinearAlgebra.Matrix.Block

Cited by

1 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingDecidableEqFintypeLinearOrderInvertible