Theorems · Theorem · linear algebra
Matrix.posSemidef_diagonal_iff
∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
[inst_4 : DecidableEq n] {d : n → R}, (Matrix.diagonal d).PosSemidef ↔ ∀ (i : n), 0 ≤ d iA diagonal matrix is positive semidefinite iff its diagonal entries are nonnegative.
- Defined in
- Mathlib.LinearAlgebra.Matrix.PosDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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- PartialOrderstatement and proof · cited by 6,410
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- MulZeroClass.mul_zeroproof · cited by 2,091
- StarRingstatement and proof · cited by 1,686
- MulZeroClass.zero_mulproof · cited by 1,625
- Star.starproof · cited by 1,082
- Finsupp.singleproof · cited by 943
- StarOrderedRingstatement and proof · cited by 587
- Finsupp.sumproof · cited by 481
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