Theorems · Theorem · linear algebra

Matrix.add_mul_mul_invOf_mul_eq_one

∀ {m : Type u_1} {n : Type u_2} {α : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : Fintype m]
  [inst_3 : DecidableEq m] [inst_4 : Ring α] (A : Matrix n n α) (U : Matrix n m α) (C : Matrix m m α) (V : Matrix m n α)
  [inst_5 : Invertible A] [inst_6 : Invertible C] [inst_7 : Invertible (⅟C + V * ⅟A * U)],
  (A + U * C * V) * (⅟A - ⅟A * U * ⅟(⅟C + V * ⅟A * U) * V * ⅟A) = 1

Defined in

Mathlib.LinearAlgebra.Matrix.Invertible

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqFintypeDecidableEqRingInvertibleInvertibleInvertible