Theorems · Theorem · linear algebra
Matrix.adjugate_mul
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A : Matrix n n α),
A.adjugate * A = A.det • 1- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 98 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.
Cites13
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
- Matrix.transposeproof · cited by 389
- Matrix.adjugatestatement and proof · cited by 64
- Matrix.det_transposeproof · cited by 51
- Matrix.transpose_transposeproof · cited by 33
- Matrix.transpose_oneproof · cited by 22
- Matrix.transpose_mulproof · cited by 14
- Matrix.mul_adjugateproof · cited by 10
- Matrix.transpose_smulproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Matrix.aeval_self_charpolyproof · cited by 6
- Matrix.isRegular_of_isLeftRegular_detproof · cited by 3
- Ideal.FinrankQuotientMap.span_eq_topproof · cited by 1
- Matrix.det_smul_adjugate_adjugateproof · cited by 1
- Matrix.det_eq_zero_of_mulVec_eq_zero_of_mem_nonZeroDivisorsproof · cited by 0
- Polynomial.adjSylvester_comp_sylveserMapproof · cited by 0