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Theorems · Theorem · linear algebra

Matrix.IsDiag.diagonal_diag

∀ {α : Type u_1} {n : Type u_4} [inst : Zero α] [inst_1 : DecidableEq n] {A : Matrix n n α},
  A.IsDiag → Matrix.diagonal A.diag = A

Diagonal matrices are generated by the Matrix.diagonal of their Matrix.diag.

Defined in
Mathlib.LinearAlgebra.Matrix.IsDiag
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
ZeroDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Matrix.isDiag_iff_diagonal_diag · cited by 0Matrix.isDiag_iff_diagona…Matrix · cited by 4303MatrixMatrix.ext · cited by 540Matrix.extMatrix.diagonal · cited by 314Matrix.diagonalMatrix.diagonal_apply_eq · cited by 64Matrix.diagonal_apply_eqMatrix.diag · cited by 61Matrix.diagMatrix.diagonal_apply_ne · cited by 50Matrix.diagonal_apply_neDecidable.eq_or_ne · cited by 28Decidable.eq_or_neMatrix.IsDiag · cited by 25Matrix.IsDiagIsDiag.diagonal_diagCITED BYCITES

Cites8

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Cited by1

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