Leading principal minors are positive

Reference no: EM131834626

A real matrix M (not necessarily symmetric) is defined to be positive definite if x' Mx > 0 for any nonzero x. Is it true that the matrix M is positive definite if all eigenvalues of M are real and positive or if all its leading principal minors are positive? If not, how do you check its positive definiteness?

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Reference no: EM131834626

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