Mathlib Map

Theorems · Theorem · linear algebra

Matrix.nonsingular_transpose_iff

∀ {n : Type u_1} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
  {A : Matrix n n R}, A.transpose.Nonsingular ↔ A.Nonsingular
Defined in
Mathlib.LinearAlgebra.Matrix.SemiringInverse
Cited by
2 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeDecidableEqCommSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.Nonsingular.transpose · cited by 1Nonsingular.transposeMatrix.Nonsingular.of_transpose · cited by 0Nonsingular.of_transposeCommSemiring · cited by 10911CommSemiringFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMatrix.transpose · cited by 389Matrix.transposeMatrix.Nonsingular · cited by 27Matrix.NonsingularMatrix.IsDetpBalanced · cited by 21Matrix.IsDetpBalancedMatrix.nonsingular_transpose_…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.