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Theorems · Theorem · linear algebra

Matrix.diagonal_apply_ne

∀ {n : Type u_3} {α : Type v} [inst : DecidableEq n] [inst_1 : Zero α] (d : n → α) {i j : n},
  i ≠ j → Matrix.diagonal d i j = 0
Defined in
Mathlib.Data.Matrix.Diagonal
Cited by
50 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
DecidableEqZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.one_apply_ne · cited by 39Matrix.one_apply_neMatrix.diagonal_transpose · cited by 17Matrix.diagonal_transposeMatrix.diagonal_mul_diagonal · cited by 9Matrix.diagonal_mul_diago…Matrix.diagonal_apply_ne' · cited by 8Matrix.diagonal_apply_ne'Matrix.charmatrix_apply_ne · cited by 6Matrix.charmatrix_apply_neRootPairing.GeckConstruction.h_eq_diagonal · cited by 4GeckConstruction.h_eq_dia…isCusp_SL2Z_iff · cited by 3isCusp_SL2Z_iffMatrix.submatrix_diagonal · cited by 3Matrix.submatrix_diagonalMatrix.frobenius_nnnorm_diagonal · cited by 2Matrix.frobenius_nnnorm_d…Matrix.isAddUnit_mul · cited by 2Matrix.isAddUnit_mulRootPairing.GeckConstruction.lie_h_e · cited by 2GeckConstruction.lie_h_eMatrix.eval_charpoly · cited by 2Matrix.eval_charpolyModule.Basis.toMatrix_unitsSMul · cited by 2Basis.toMatrix_unitsSMulMatrix.diagonal_neg · cited by 2Matrix.diagonal_negMatrix.diagonal_smul · cited by 2Matrix.diagonal_smulMatrix.diagonal · cited by 314Matrix.diagonalMatrix.diagonal_apply_neCITED BYCITES

Cites1

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Cited by50

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