Theorems · Theorem · linear algebra
Matrix.updateRow_apply
∀ {m : Type u_2} {n : Type u_3} {α : Type v} {M : Matrix m n α} {i : m} {j : n} {b : n → α} [inst : DecidableEq m]
{i' : m}, M.updateRow i b i' j = if i' = i then b j else M i' j- Defined in
- Mathlib.LinearAlgebra.Matrix.RowCol
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- Matrix.updateRowstatement and proof · cited by 63
- Matrix.updateRow_selfproof · cited by 19
- Matrix.updateRow_neproof · cited by 16
Cited by9
Results whose statement or proof uses this declaration.
- Matrix.updateRow_transposeproof · cited by 12
- Matrix.updateCol_transposeproof · cited by 5
- Matrix.adjugate_transposeproof · cited by 5
- Matrix.updateRow_submatrix_equivproof · cited by 4
- Matrix.map_updateRowproof · cited by 2
- Polynomial.sylvesterDeriv_updateRowproof · cited by 1
- Matrix.det_eq_of_forall_row_eq_smul_add_const_auxproof · cited by 1
- Matrix.submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_detproof · cited by 1
- Matrix.det_eq_sum_column_mul_submatrix_succAbove_succAbove_detproof · cited by 1