Theorems · Theorem · linear algebra
Matrix.det_one
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R], Matrix.det 1 = 1- Cited by
- 35 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.
Cites7
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
- Matrix.detstatement and proof · cited by 665
- Finset.prod_const_oneproof · cited by 100
- Matrix.det_diagonalproof · cited by 27
- Matrix.diagonal_oneproof · cited by 13
Cited by36
Results whose statement or proof uses this declaration.
- Matrix.detMonoidHomproof · cited by 6
- Matrix.det_of_mem_unitaryproof · cited by 4
- Module.Basis.det_selfproof · cited by 4
- Matrix.IsHadamard.det_mul_star_detproof · cited by 3
- Matrix.det_mvPolynomialX_ne_zeroproof · cited by 3
- exteriorPower.ιMultiDual_apply_diagproof · cited by 3
- Matrix.isUnit_charpolyRev_of_isNilpotentproof · cited by 2
- Matrix.det_fromBlocks₁₁proof · cited by 2
- Matrix.TransvectionStruct.det_toMatrix_prodproof · cited by 2
- Module.Basis.det_comp_basisproof · cited by 2
- Matrix.det_detproof · cited by 1
- CongruenceSubgroup.exists_Gamma_le_conjproof · cited by 1