Theorems · Theorem · linear algebra
Matrix.single_mulVec_eq
∀ {n : Type u_3} {α : Type u_7} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : NonAssocSemiring α] (i j : n)
(b : α) (w : n → α), (Matrix.single i j b).mulVec w = (b * w j) • Pi.single i 1- Defined in
- Mathlib.Data.Matrix.Basis
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 73 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.
- Fintypestatement and proof · cited by 7,736
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- NonAssocSemiringstatement and proof · cited by 805
- Pi.singlestatement · cited by 518
- Matrix.mulVecstatement · cited by 267
- mul_iteproof · cited by 159
- Matrix.singlestatement · cited by 129
- Pi.single_applyproof · cited by 78
- Function.update_applyproof · cited by 23
- Matrix.single_mulVecproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- SL2Gen.transvection_mem_lineStabproof · cited by 1
- Matrix.SpecialLinearGroup.transvection_mulVec_single_otherproof · cited by 0
- Matrix.SpecialLinearGroup.transvection_mulVec_single_selfproof · cited by 0
- Matrix.SpecialLinearGroup.transvection_smul_single_fstproof · cited by 0
- Matrix.SpecialLinearGroup.transvection_smul_single_sndproof · cited by 0