Theorems · Theorem · linear algebra
Matrix.diagonal_transpose
∀ {n : Type u_3} {α : Type v} [inst : DecidableEq n] [inst_1 : Zero α] (v : n → α),
(Matrix.diagonal v).transpose = Matrix.diagonal v- Defined in
- Mathlib.Data.Matrix.Diagonal
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- DecidableEqZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Matrixstatement · cited by 4,303
- Matrix.extproof · cited by 540
- Matrix.transposestatement · cited by 389
- Matrix.ofproof · cited by 336
- Matrix.diagonalstatement and proof · cited by 314
- Matrix.diagonal_apply_eqproof · cited by 64
- Matrix.diagonal_apply_neproof · cited by 50
- eq_comm_eqproof · cited by 17
- Matrix.diagonal.congr_simpproof · cited by 12
Cited by17
Results whose statement or proof uses this declaration.
- Matrix.transpose_oneproof · cited by 22
- Matrix.mul_diagonalproof · cited by 15
- Matrix.transpose_eq_diagonalproof · cited by 4
- Matrix.transpose_natCastproof · cited by 2
- Matrix.diagonal_conjTransposeproof · cited by 2
- Matrix.cRank_diagonalproof · cited by 1
- Matrix.adjugate_diagonalproof · cited by 1
- RootPairing.Base.exists_cartanMatrix_diagaonal_mul_posDefproof · cited by 1
- Matrix.charmatrix_transposeproof · cited by 1
- Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspaceproof · cited by 1
- Matrix.isSymm_diagonalproof · cited by 1
- Matrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigenproof · cited by 1