Theorems · Theorem · linear algebra
Matrix.eigenvalues_conjTranspose_mul_self_nonneg
∀ {m : Type u_1} {n : Type u_2} {𝕜 : Type u_3} [inst : Fintype m] [inst_1 : Fintype n] [inst_2 : RCLike 𝕜]
(A : Matrix m n 𝕜) [inst_3 : DecidableEq n] (i : n), 0 ≤ ⋯.eigenvalues i- Defined in
- Mathlib.Analysis.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- Matrix.conjTransposestatement · cited by 202
- Matrix.IsHermitian.eigenvaluesstatement · cited by 34
- Matrix.PosSemidef.eigenvalues_nonnegproof · cited by 6
- Matrix.posSemidef_conjTranspose_mul_selfproof · cited by 3
- Matrix.isHermitian_conjTranspose_mul_selfstatement · cited by 2
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