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Theorems · Theorem · linear algebra

Matrix.trace_neg

∀ {n : Type u_3} {R : Type u_6} [inst : Fintype n] [inst_1 : AddCommGroup R] (A : Matrix n n R), (-A).trace = -A.trace
Defined in
Mathlib.LinearAlgebra.Matrix.Trace
Cited by
4 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
FintypeAddCommGroup
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Around this declaration

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

Matrix.isElliptic_neg_iff · cited by 3Matrix.isElliptic_neg_iffMatrix.IsParabolic.neg · cited by 2IsParabolic.negMatrix.isHyperbolic_neg_iff · cited by 2Matrix.isHyperbolic_neg_i…UpperHalfPlane.fixedPt_neg · cited by 1UpperHalfPlane.fixedPt_negAddCommGroup · cited by 12871AddCommGroupFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMatrix.trace · cited by 114Matrix.traceFinset.sum_neg_distrib · cited by 65Finset.sum_neg_distribMatrix.trace_negCITED BYCITES

Cites5

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Cited by4

Results whose statement or proof uses this declaration.