Theorems · Theorem · linear algebra

Matrix.det_le

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [Nontrivial R] [inst_2 : CommRing S] [inst_3 : LinearOrder S]
  [IsStrictOrderedRing S] {n : Type u_3} [inst_5 : Fintype n] [inst_6 : DecidableEq n] {A : Matrix n n R}
  {abv : AbsoluteValue R S} {x : S},
  (∀ (i j : n), abv (A i j) ≤ x) → abv A.det ≤ (Fintype.card n).factorial • x ^ Fintype.card n

Defined in

Mathlib.LinearAlgebra.Matrix.AbsoluteValue

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingNontrivialCommRingLinearOrderIsStrictOrderedRingFintypeDecidableEq