Theorems · Theorem · linear algebra
Matrix.Nonsingular.of_linearIndependent_row
∀ {R : Type u_1} {n : Type u_3} [inst : CommSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n]
{A : Matrix n n R}, LinearIndependent R A.row → A.Nonsingular- Defined in
- Mathlib.LinearAlgebra.Matrix.Nonsingular
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LinearIndependentstatement and proof · cited by 560
- Matrix.rowstatement and proof · cited by 40
- Matrix.Nonsingularstatement · cited by 27
- Matrix.Nonsingular.of_linearIndependent_colproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.linearIndependent_row_iffproof · cited by 2
- Matrix.Nonsingular.of_rightRegularproof · cited by 0