Theorems · Theorem · linear algebra
Matrix.det_smul
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (A : Matrix n n R)
(c : R), (c • A).det = c ^ Fintype.card n * A.det- Cited by
- 11 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Fintype.cardstatement and proof · cited by 1,386
- Matrix.detstatement and proof · cited by 665
- Matrix.diagonalproof · cited by 314
- Finset.prod_constproof · cited by 154
- Matrix.det_mulproof · cited by 51
- Matrix.det_diagonalproof · cited by 27
- Matrix.smul_eq_diagonal_mulproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- Matrix.det_negproof · cited by 14
- Matrix.det_eq_sign_charpoly_coeffproof · cited by 5
- LinearMap.det_smulproof · cited by 5
- Matrix.det_smul_of_towerproof · cited by 4
- Matrix.reverse_charpolyproof · cited by 3
- Matrix.IsHadamard.det_mul_star_detproof · cited by 3
- Matrix.IsHadamard.of_mul_conjTransposeproof · cited by 1
- LinearMap.normDet_smulproof · cited by 1
- Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_of_rootsproof · cited by 1
- Matrix.J_det_mul_J_detproof · cited by 1
- Matrix.det_adjugateproof · cited by 0