Theorems · Theorem · linear algebra
Matrix.det_neg_eq_smul
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (A : Matrix n n R),
(-A).det = (-1) ^ Fintype.card n • A.detA variant of Matrix.det_neg with scalar multiplication by Units ℤ instead of multiplication
by R.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Unitsstatement and proof · cited by 2,804
- Fintype.cardstatement · cited by 1,386
- one_smulproof · cited by 1,374
- Matrix.detstatement and proof · cited by 665
- Units.neg_smulproof · cited by 27
- Matrix.det_smul_of_towerproof · cited by 4
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