Theorems · Theorem · linear algebra
Matrix.one_apply_eq
∀ {n : Type u_3} {α : Type v} [inst : DecidableEq n] [inst_1 : Zero α] [inst_2 : One α] (i : n), 1 i i = 1- Defined in
- Mathlib.Data.Matrix.Diagonal
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- DecidableEqZeroOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement · cited by 4,303
- Matrix.diagonal_apply_eqproof · cited by 64
Cited by35
Results whose statement or proof uses this declaration.
- UpperHalfPlane.denom_oneproof · cited by 3
- Matrix.matPolyEquiv_charmatrixproof · cited by 3
- Matrix.Nonsingular.linearIndependent_colproof · cited by 2
- Algebra.Norm.Transitivity.mul_auxMat_toSquareBlock_eqproof · cited by 2
- Matrix.TransvectionStruct.toMatrix_sumInlproof · cited by 2
- Matrix.toMvPolynomial_oneproof · cited by 1
- Ideal.single_mem_jacobson_matrixproof · cited by 1
- Matrix.diag2_decomposeproof · cited by 1
- Matrix.transvection_mem_commutator₁proof · cited by 1
- Matrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigenproof · cited by 1
- Matrix.mul_adjp_add_detpproof · cited by 1
- Matrix.commutator_diag2_transvectionproof · cited by 1