Theorems · Theorem · linear algebra
Matrix.toLinAlgEquiv_apply
∀ {R : Type u_1} [inst : CommSemiring R] {n : Type u_4} [inst_1 : Fintype n] [inst_2 : DecidableEq n] {M₁ : Type u_5}
[inst_3 : AddCommMonoid M₁] [inst_4 : Module R M₁] (v₁ : Module.Basis n R M₁) (M : Matrix n n R) (v : M₁),
((Matrix.toLinAlgEquiv v₁) M) v = ∑ j, M.mulVec (⇑(v₁.repr v)) j • v₁ j- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Finsuppstatement · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- LinearEquivstatement · cited by 3,317
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