Theorems · Theorem · linear algebra

Algebra.smulTower_leftMulMatrix_algebraMap_ne

∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Semiring T]
  [inst_3 : Algebra R S] [inst_4 : Algebra S T] [inst_5 : Algebra R T] [inst_6 : IsScalarTower R S T] {m : Type u_4}
  {n : Type u_5} [inst_7 : Fintype m] [inst_8 : Fintype n] [inst_9 : DecidableEq m] [inst_10 : DecidableEq n]
  (b : Module.Basis m R S) (c : Module.Basis n S T) (x : S) (i j : m) {k k' : n},
  k ≠ k' → (Algebra.leftMulMatrix (b.smulTower c)) ((algebraMap S T) x) (i, k) (j, k') = 0

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringSemiringAlgebraAlgebraAlgebraIsScalarTowerFintypeFintypeDecidableEqDecidableEq