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Theorems · Theorem

Matrix.mulVec_cons

∀ {n : ℕ} {m' : Type uₘ} {α : Type u_1} [inst : NonUnitalCommSemiring α] (A : m' → Fin n.succ → α) (x : α)
  (v : Fin n → α),
  (Matrix.of A).mulVec (Matrix.vecCons x v) = x • Matrix.vecHead ∘ A + (Matrix.of (Matrix.vecTail ∘ A)).mulVec v
Defined in
Mathlib.LinearAlgebra.Matrix.Notation
Cited by
1 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalCommSemiring
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Around this declaration

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QuadraticAlgebra.det_toLinearMap_eq_norm · cited by 0QuadraticAlgebra.det_toLi…DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivMatrix · cited by 4303Matrixmul_comm · cited by 2262mul_commMatrix.vecCons · cited by 852Matrix.vecConsMatrix.of · cited by 336Matrix.ofMatrix.mulVec · cited by 267Matrix.mulVecdotProduct · cited by 194dotProductMatrix.vecTail · cited by 39Matrix.vecTailMatrix.vecHead · cited by 34Matrix.vecHeadNonUnitalCommSemiring · cited by 29NonUnitalCommSemiringMatrix.dotProduct_cons · cited by 5Matrix.dotProduct_consMatrix.mulVec_consCITED BYCITES

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Cited by1

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