Theorems · Theorem · linear algebra
PiToModule.fromMatrix_apply
∀ {ι : Type u_1} [inst : Fintype ι] {M : Type u_2} [inst_1 : AddCommGroup M] (R : Type u_3) [inst_2 : CommRing R]
[inst_3 : Module R M] (b : ι → M) [inst_4 : DecidableEq ι] (A : Matrix ι ι R) (w : ι → R),
((PiToModule.fromMatrix R b) A) w = (Fintype.linearCombination R b) (A.mulVec w)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.mulVecstatement · cited by 267
- Fintype.linearCombinationstatement · cited by 26
- PiToModule.fromMatrixstatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- PiToModule.fromMatrix_apply_single_oneproof · cited by 1