Theorems · Theorem · linear algebra
Matrix.det_eq_zero_of_column_eq_zero
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {A : Matrix n n R}
(j : n), (∀ (i : n), A i j = 0) → A.det = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.detstatement · cited by 665
- Matrix.det_transposeproof · cited by 51
- Matrix.det_eq_zero_of_row_eq_zeroproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.resultant_zero_rightproof · cited by 3
- exteriorPower.ιMultiDual_apply_nondiagproof · cited by 3
- Matrix.derivative_det_one_add_X_smul_auxproof · cited by 1
- Matrix.adjugate_zeroproof · cited by 0
- Matrix.cramer_zeroproof · cited by 0