Theorems · Theorem · linear algebra

Matrix.det_smul_of_tower

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {α : Type u_3}
  [inst_3 : Monoid α] [inst_4 : MulAction α R] [IsScalarTower α R R] [SMulCommClass α R R] (c : α) (A : Matrix n n R),
  (c • A).det = c ^ Fintype.card n • A.det

Defined in

Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Cited by

4 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommRingMonoidMulActionIsScalarTowerSMulCommClass