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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.

Matrix.transpose_one · cited by 22Matrix.transpose_oneMatrix.mul_diagonal · cited by 15Matrix.mul_diagonalMatrix.transpose_eq_diagonal · cited by 4Matrix.transpose_eq_diago…Matrix.transpose_natCast · cited by 2Matrix.transpose_natCastMatrix.diagonal_conjTranspose · cited by 2Matrix.diagonal_conjTrans…Matrix.cRank_diagonal · cited by 1Matrix.cRank_diagonalMatrix.adjugate_diagonal · cited by 1Matrix.adjugate_diagonalRootPairing.Base.exists_cartanMatrix_diagaonal_mul_posDef · cited by 1Base.exists_cartanMatrix_…Matrix.charmatrix_transpose · cited by 1Matrix.charmatrix_transpo…Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace · cited by 1Matrix.maxGenEigenspace_t…Matrix.isSymm_diagonal · cited by 1Matrix.isSymm_diagonalMatrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigen · cited by 1Matrix.lt_two_mul_of_mul_…Matrix.transpose_intCast · cited by 1Matrix.transpose_intCastMatrix.isHermitian_diagonal_iff · cited by 1Matrix.isHermitian_diagon…LieAlgebra.Orthogonal.indefiniteDiagonal_transform · cited by 0Orthogonal.indefiniteDiag…DFunLike.coe · cited by 62936DFunLike.coeMatrix · cited by 4303MatrixMatrix.ext · cited by 540Matrix.extMatrix.transpose · cited by 389Matrix.transposeMatrix.of · cited by 336Matrix.ofMatrix.diagonal · cited by 314Matrix.diagonalMatrix.diagonal_apply_eq · cited by 64Matrix.diagonal_apply_eqMatrix.diagonal_apply_ne · cited by 50Matrix.diagonal_apply_neeq_comm_eq · cited by 17eq_comm_eqMatrix.diagonal.congr_simp · cited by 12diagonal.congr_simpMatrix.diagonal_transposeCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by17

Results whose statement or proof uses this declaration.