Theorems · Theorem · linear algebra
Matrix.Nonsingular.of_linearIndependent_col
∀ {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.col → A.NonsingularIf the columns of a square matrix are linearly independent, then the matrix is nonsingular.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Nonsingular
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites60
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Fintypestatement and proof · cited by 7,736
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- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- Equiv.symmproof · cited by 3,681
- Finset.univproof · cited by 3,473
- Unitsproof · cited by 2,804
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.Nonsingular.of_linearIndependent_rowproof · cited by 2
- Matrix.linearIndependent_col_iffproof · cited by 2
- Matrix.Nonsingular.of_leftRegularproof · cited by 0