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Theorems · Theorem · linear algebra

Matrix.PosSemidef.zpow

∀ {n : Type u_2} {R' : Type u_4} [inst : CommRing R'] [inst_1 : PartialOrder R'] [inst_2 : StarRing R']
  [inst_3 : Fintype n] [StarOrderedRing R'] [inst_5 : DecidableEq n] {M : Matrix n n R'},
  M.PosSemidef → ∀ (z : ℤ), (M ^ z).PosSemidef
Defined in
Mathlib.LinearAlgebra.Matrix.PosDef
Cited by
0 results in Mathlib
Foundations
Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingPartialOrderStarRingFintypeStarOrderedRingDecidableEq
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CommRing · cited by 17173CommRingFintype · cited by 7736FintypePartialOrder · cited by 6410PartialOrderMatrix · cited by 4303MatrixStarRing · cited by 1686StarRingStarOrderedRing · cited by 587StarOrderedRingzpow_natCast · cited by 271zpow_natCastMatrix.PosSemidef · cited by 76Matrix.PosSemidefMatrix.zpow_neg_natCast · cited by 6Matrix.zpow_neg_natCastMatrix.PosSemidef.inv · cited by 2PosSemidef.invMatrix.PosSemidef.pow · cited by 1PosSemidef.powPosSemidef.zpowCITED BYCITES

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