Theorems · Theorem · linear algebra
Matrix.mulVec_diagonal
∀ {m : Type u_2} {α : Type v} [inst : NonUnitalNonAssocSemiring α] [inst_1 : Fintype m] [inst_2 : DecidableEq m]
(v w : m → α) (x : m), (Matrix.diagonal v).mulVec w x = v x * w x- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Matrix.diagonalstatement · cited by 314
- Matrix.mulVecstatement · cited by 267
- diagonal_dotProductproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Matrix.one_mulVecproof · cited by 12
- Matrix.diagonal_mulVec_singleproof · cited by 3
- Matrix.diagonal_const_mulVecproof · cited by 3
- Matrix.proj_diagonalproof · cited by 1
- Matrix.diagonal_toLin'proof · cited by 1
- Matrix.l2_opNorm_diagonalproof · cited by 1
- SimpleGraph.degMatrix_mulVec_applyproof · cited by 1
- SimpleGraph.dotProduct_mulVec_degMatrixproof · cited by 1