Theorems · Theorem · linear algebra

LinearMap.det_toMatrix_eq_det_toMatrix

∀ {M : Type u_2} [inst : AddCommGroup M] {ι : Type u_4} [inst_1 : DecidableEq ι] [inst_2 : Fintype ι] {A : Type u_5}
  [inst_3 : CommRing A] [inst_4 : Module A M] {κ : Type u_6} [inst_5 : Fintype κ] [inst_6 : DecidableEq κ]
  (b : Module.Basis ι A M) (c : Module.Basis κ A M) (f : M →ₗ[A] M),
  ((LinearMap.toMatrix b b) f).det = ((LinearMap.toMatrix c c) f).det

The determinant of LinearMap.toMatrix does not depend on the choice of basis.

Defined in

Mathlib.LinearAlgebra.Determinant

Cited by

2 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupDecidableEqFintypeCommRingModuleFintypeDecidableEq