Theorems · Theorem · linear algebra
Matrix.isUnit_transpose
∀ {n : Type u_2} {α : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring α]
(A : Matrix n n α), IsUnit A.transpose ↔ IsUnit A- Defined in
- Mathlib.LinearAlgebra.Matrix.Invertible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- IsUnitstatement · cited by 1,602
- Invertibleproof · cited by 549
- Matrix.transposestatement and proof · cited by 389
- Equiv.nonempty_congrproof · cited by 47
- Matrix.transposeInvertibleEquivInvertibleproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.mulVec_injective_iff_isUnitproof · cited by 4
- Matrix.linearIndependent_cols_iff_isUnitproof · cited by 1