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Theorems · Theorem · linear algebra

Matrix.trace_vecMulVec

∀ {n : Type u_3} {R : Type u_6} [inst : Fintype n] [inst_1 : NonUnitalNonAssocSemiring R] (a b : n → R),
  (Matrix.vecMulVec a b).trace = a ⬝ᵥ b
Defined in
Mathlib.LinearAlgebra.Matrix.Trace
Cited by
1 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeNonUnitalNonAssocSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearMap.trace_smulRight · cited by 0LinearMap.trace_smulRightFintype · cited by 7736FintypeMatrix · cited by 4303MatrixNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringdotProduct · cited by 194dotProductMatrix.trace · cited by 114Matrix.traceMatrix.vecMulVec · cited by 52Matrix.vecMulVecMatrix.vecMulVec_eq · cited by 7Matrix.vecMulVec_eqMatrix.trace_replicateCol_mul_replicateRow · cited by 1Matrix.trace_replicateCol…Matrix.trace_vecMulVecCITED BYCITES

Cites8

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Cited by1

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