Theorems · Theorem · linear algebra

Matrix.isDetpBalanced_submatrix_equiv_iff

∀ {n : Type u_1} {m : Type u_2} {R : Type u_3} [inst : Fintype m] [inst_1 : Fintype n] [inst_2 : DecidableEq m]
  [inst_3 : DecidableEq n] [inst_4 : CommSemiring R] {A : Matrix n n R} {a b : R} {e₁ e₂ : m ≃ n},
  (A.submatrix ⇑e₁ ⇑e₂).IsDetpBalanced a b ↔ A.IsDetpBalanced a b

Defined in

Mathlib.LinearAlgebra.Matrix.SemiringInverse

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFintypeDecidableEqDecidableEqCommSemiring