Theorems · Theorem · linear algebra
Matrix.det_of_isUpperTriangular
∀ {m : Type u_3} {R : Type v} {M : Matrix m m R} [inst : CommRing R] [inst_1 : DecidableEq m] [inst_2 : Fintype m]
[inst_3 : LinearOrder m], M.IsUpperTriangular → M.det = ∏ i, M i i- Defined in
- Mathlib.LinearAlgebra.Matrix.Block
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- Matrix.detstatement and proof · cited by 665
- Finset.prod_congrproof · cited by 646
- Classical.decEqproof · cited by 134
- Matrix.toSquareBlockproof · cited by 15
- Matrix.IsUpperTriangularstatement and proof · cited by 8
- Finset.image_idproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Matrix.det_of_isLowerTriangularproof · cited by 2
- InnerProductSpace.gramSchmidtOrthonormalBasis_detproof · cited by 2
- Polynomial.det_taylorLinearEquiv_toLinearMapproof · cited by 1
- Matrix.IsPivotedBy.rank_eqproof · cited by 1
- Matrix.det_matrixOfPolynomialsproof · cited by 1
- Matrix.charpoly_of_isUpperTriangularproof · cited by 1
- Matrix.rank_mul_eq_right_of_isUpperTriangularproof · cited by 0
- Matrix.det_of_upperTriangularproof · cited by 0