Theorems · Theorem · linear algebra
Matrix.cramer_transpose_row_self
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A : Matrix n n α)
(i : n), A.transpose.cramer (A i) = Pi.single i A.det- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.detstatement and proof · cited by 665
- Pi.singlestatement and proof · cited by 518
- Matrix.transposestatement and proof · cited by 389
- Matrix.det.congr_simpproof · cited by 91
- Pi.single_applyproof · cited by 78
- Matrix.updateRowproof · cited by 63
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.mul_adjugateproof · cited by 10
- Matrix.cramer_row_selfproof · cited by 1