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A symmetric m ×m matrix K satisfying ∀x ∈ c m : 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≠∅, is positive (semi-) definite if for all m ∈ n and all x 1, …, 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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(2011). Positive Semidefinite. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30164-8_646
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DOI: https://doi.org/10.1007/978-0-387-30164-8_646
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30768-8
Online ISBN: 978-0-387-30164-8
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