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Reverted 1 edit by 202.28.119.47 (talk) |
Explicitly state that positive definite matrices are invertible. Tag: Reverted |
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Positive-definite and positive-semidefinite matrices can be characterized in many ways, which may explain the importance of the concept in various parts of mathematics. A matrix {{mvar|M}} is positive-definite if and only if it satisfies any of the following equivalent conditions.
* {{mvar|M}} is [[Invertible matrix|invertible]].
* {{mvar|M}} is [[congruent matrices|congruent]] with a [[diagonal matrix]] with positive real entries.
* {{mvar|M}} is symmetric or Hermitian, and all its [[eigenvalue]]s are real and positive.
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