Theorems · Theorem · linear algebra
Matrix.proj_diagonal
∀ {n : Type u_1} [inst : Fintype n] [inst_1 : DecidableEq n] {R : Type v} [inst_2 : CommSemiring R] (i : n) (w : n → R),
LinearMap.proj i ∘ₗ Matrix.toLin' (Matrix.diagonal w) = w i • LinearMap.proj i- Defined in
- Mathlib.LinearAlgebra.Matrix.Diagonal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- Matrix.diagonalstatement · cited by 314
- Matrix.toLin'statement · cited by 86
- LinearMap.projstatement · cited by 71
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.ker_diagonal_toLin'proof · cited by 0