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Positive definite matrix

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A positive definite matrix has at least one matrix square root. ... A Hermitian (or symmetric) matrix is positive definite iff all its eigenvalues are positive. Therefore, a general complex (respectively, real) matrix is positive definite iff its Hermitian (or symmetric) part has all positive eigenvalues.
https://mathworld.wolfram.com › Po...
A matrix is positive semi-definite if it satisfies similar equivalent conditions where "positive" is replaced by "nonnegative" and "invertible matrix" is ...
In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, ...

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2020年7月21日 — A^{-1} is positive definite. · A has a unique symmetric positive definite square root X , where a square root is a matrix X such that X^2 = A .

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