Theorems · Theorem · linear algebra

Matrix.toLin_apply_eq_zero_iff

∀ {m : Type u_3} {n : Type u_4} [inst : Fintype n] [inst_1 : DecidableEq n] {R : Type u_7} {M₁ : Type u_8}
  {M₂ : Type u_9} [inst_2 : Finite m] [inst_3 : CommRing R] [inst_4 : AddCommGroup M₁] [inst_5 : AddCommGroup M₂]
  [inst_6 : Module R M₁] [inst_7 : Module R M₂] {v₁ : Module.Basis n R M₁} {v₂ : Module.Basis m R M₂} {A : Matrix m n R}
  {x : M₁}, ((Matrix.toLin v₁ v₂) A) x = 0 ↔ ∀ (j : m), A.mulVec (⇑(v₁.repr x)) j = 0

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

1 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqFiniteCommRingAddCommGroupAddCommGroupModuleModule