Theorems · Theorem · linear algebra
Matrix.linearIndependent_col_iff_row
∀ {R : Type u_1} {n : Type u_3} [inst : CommSemiring R] {A : Matrix n n R} [IsCancelAdd R] [Finite n],
LinearIndependent R A.col ↔ LinearIndependent R A.rowhttps://mathoverflow.net/questions/511862/transpose-symmetry-of-injectivity-of-linear-maps-over-semirings
asks whether this is still true without IsCancelAdd R.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Nonsingular
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- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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- CommSemiringstatement and proof · cited by 10,911
- Fintypeproof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finitestatement and proof · cited by 3,029
- LinearIndependentstatement and proof · cited by 560
- Fintype.ofFiniteproof · cited by 255
- IsCancelAddstatement and proof · cited by 79
- Matrix.colstatement · cited by 56
- Matrix.rowstatement and proof · cited by 40
- Matrix.Nonsingularproof · cited by 27
- Matrix.linearIndependent_col_iffproof · cited by 2
- Matrix.linearIndependent_row_iffproof · cited by 2
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