Theorems · Theorem · linear algebra
Matrix.Module.single_smul
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : Ring R] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] (i j : ι) (r : R) (v : ι → M),
Matrix.single i j r • v = Pi.single i (r • v j)- Defined in
- Mathlib.LinearAlgebra.Matrix.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- Matrixstatement · cited by 4,303
- eq_or_neproof · cited by 1,117
- zero_smulproof · cited by 716
- Pi.singlestatement and proof · cited by 518
- Pi.single_eq_sameproof · cited by 144
- Matrix.singlestatement · cited by 129
- Pi.single_eq_of_ne'proof · cited by 33
- Fintype.sum_eq_singleproof · cited by 16
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