Theorems · Theorem · linear algebra

AlgHom.map_det

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {S : Type w}
  [inst_3 : CommRing S] [inst_4 : Algebra R S] {T : Type z} [inst_5 : CommRing T] [inst_6 : Algebra R T] (f : S →ₐ[R] T)
  (M : Matrix n n S), f M.det = (f.mapMatrix M).det

Defined in

Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Cited by

6 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommRingCommRingAlgebraCommRingAlgebra