Theorems · Theorem · linear algebra
Matrix.linearIndependent_cols_iff_isUnit
∀ {m : Type u} [inst : DecidableEq m] {K : Type u_3} [inst_1 : Field K] [inst_2 : Fintype m] {A : Matrix m m K},
LinearIndependent K A.col ↔ IsUnit A- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFieldFintype
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.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Matrixstatement and proof · cited by 4,303
- IsUnitstatement and proof · cited by 1,602
- LinearIndependentstatement and proof · cited by 560
- Matrix.colstatement · cited by 56
- Matrix.row_transposeproof · cited by 3
- Matrix.linearIndependent_rows_iff_isUnitproof · cited by 2
- Matrix.isUnit_transposeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.linearIndependent_cols_of_invertibleproof · cited by 0