Theorems · Theorem · linear algebra
Matrix.linearIndependent_col_iff
∀ {R : Type u_1} {n : Type u_3} [inst : CommSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {A : Matrix n n R}
[IsCancelAdd R], LinearIndependent R A.col ↔ 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.
Cites9
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 · cited by 560
- IsCancelAddstatement and proof · cited by 79
- Matrix.colstatement · cited by 56
- Matrix.Nonsingularstatement and proof · cited by 27
- Matrix.Nonsingular.of_linearIndependent_colproof · cited by 3
- Matrix.Nonsingular.linearIndependent_colproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.isLeftRegular_iff_nonsingularproof · cited by 3
- Matrix.linearIndependent_col_iff_rowproof · cited by 0