Theorems · Theorem · linear algebra
Matrix.PosSemidef.hadamard
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {ι : Type u_3} {A B : Matrix ι ι 𝕜},
A.PosSemidef → B.PosSemidef → (A.hadamard B).PosSemidef[Schur product theorem][schur1911] (positive semidefinite version): the Hadamard (entrywise) product of positive semidefinite matrices is positive semidefinite.
- Defined in
- Mathlib.Analysis.Matrix.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 267 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
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