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Definition
A symmetric m × m matrix K satisfying ∀ x ∈ cm : x∗Kx ≥ 0 is called positive semidefinite. If the equality only holds for \(x =\vec{ 0}\) the matrix is positive definite.
A function k : X × X → c, X ≠Ø, is positive (semi-) definite if for all m ∈ n and all x1, …, x m ∈ X the m × m matrix \(\vec{K}\) with elements K ij : = k(x i , x j ) is positive (semi-) definite.
Sometimes the term strictly positive definite is used instead of positive definite, and positive definite refers then to positive semidefiniteness.
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(2017). Positive Semidefinite. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_961
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DOI: https://doi.org/10.1007/978-1-4899-7687-1_961
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