Theorems · Theorem · linear algebra
Matrix.det_mul
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (M N : Matrix n n R),
(M * N).det = M.det * N.det- Cited by
- 51 results in Mathlib
- Foundations
- Depth 89 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.
Cites44
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- Finset.univproof · cited by 3,473
- Unitsproof · cited by 2,804
- Finset.prodproof · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- Units.valproof · cited by 1,966
Cited by52
Results whose statement or proof uses this declaration.
- Matrix.det_smulproof · cited by 11
- LinearMap.normDet_eq_norm_det_toMatrix_rangeRestrictproof · cited by 8
- Matrix.detMonoidHomproof · cited by 6
- Algebra.discr_eq_det_embeddingsMatrixReindex_pow_twoproof · cited by 4
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- Matrix.det_of_mem_unitaryproof · cited by 4
- Matrix.mul_inv_revproof · cited by 4
- Matrix.det_mul_commproof · cited by 3
- Matrix.IsHadamard.det_mul_star_detproof · cited by 3
- Algebra.discr_of_matrix_vecMulproof · cited by 2
- Matrix.det_fromBlocks₁₁proof · cited by 2
- Matrix.det_kroneckerMapBilinearproof · cited by 2