Theorems · Theorem · linear algebra
Matrix.diagonal_apply_eq
∀ {n : Type u_3} {α : Type v} [inst : DecidableEq n] [inst_1 : Zero α] (d : n → α) (i : n), Matrix.diagonal d i i = d i- Defined in
- Mathlib.Data.Matrix.Diagonal
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- DecidableEqZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrix.diagonalstatement · cited by 314
Cited by64
Results whose statement or proof uses this declaration.
- Matrix.one_apply_eqproof · cited by 35
- Matrix.det_diagonalproof · cited by 27
- Matrix.diagonal_transposeproof · cited by 17
- Matrix.diagonal_mul_diagonalproof · cited by 9
- Matrix.charmatrix_apply_eqproof · cited by 8
- Matrix.center_eq_scalar_imageproof · cited by 6
- Matrix.diagonal_injectiveproof · cited by 6
- Matrix.diag_diagonalproof · cited by 4
- Matrix.submatrix_diagonalproof · cited by 3
- Matrix.trace_diagonalproof · cited by 3
- Algebra.trace_algebraMap_of_basisproof · cited by 2
- Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_centerproof · cited by 2