Qi. Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors. J. Ind. Manag. Optim., 11(4):1263-1274, 2015.H. Chen, L. Qi, Positive Definiteness and Semi-Definiteness of Even Order Symmetric Cauchy Tensors, Journal of Industrial and Management Optimization 11 (2015...
Concretely, positive semi-definiteness of some linear combination of bilinear forms {bk∆2}Nk=α1 associated, in the sense of section 2.3, to partial derivatives of order Λk, is most conveniently shown after conjugation with the matrix ∞ Nij ≡δinδjn n=0 3n(2∆2)nn! (∆2 + ...
Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques....
1.The inverse problems for positive definite and semipositive definite matrices of equation AX=B on manifold;流形上矩阵方程AX=B的正定及半正定阵的反问题 2.The new method of judgement for matrix positive definite in Euclid space;Euclid空间中矩阵正定性判别的新方法 3.Some notes on the positive def...
Positive semi - definite matrices are positive definite if and only if they are nonsingular. 正半定矩阵是正定的,当且仅当它们是非奇异矩阵。 —— 辞典例句 4. Bao Zhengding three snacks: Pa cake, slip , bean brain. 正定小吃三大宝: 扒糕、粉浆 、 豆腐脑。
From which I conclude that∇2g∇2gis positive semi-definite at(c,c)(c,c), but I want it to be positive definite. I also easily get that∇g(c,c)=0∇g(c,c)=0, so positive definiteness would imply what I want. I'm not sure what went wrong (are my calculations correct?)...
负定矩阵和半负定矩阵的定义类似。非半正定和非半负定(not positive semi-definite and not negative semi-definite)的矩阵有时称为不定(indefinite)矩阵。 等效条件 从上述定义可知,矩阵是正定的当且仅当它是正定二次型( positive-definite quadratic form)或 Hermitian 型矩阵。换句话说,矩阵是正定的当且仅当它...
A positive (semi-)definite matrix is a square matrix with the following property: (1.63)x′Ax=x′12(A+A′)x≥0,∀x. If the inequality is strictly greater, it is positive definite, otherwise positive semi-definite. From the definition, we can see that A is positive (semi-)definite...
Positive Definiteness Definition A matrix A∈Cn×n is a positive definite matrix if x∗Ax>0for any x∈Cn∖{0}A is a positive semidefinite matrix if x∗Ax≥0for any x∈Cn Note A non-Hermitian matrix A is positive (semi)definite if and only if its Hermitian part 12(A+A∗) ...
For simplicity of notation, the negative definiteness is often denoted as (10.4)A≺0. Two important identities are the following: Identity 1: Consider two n×n, symmetric positive definite matrices A and B. If A−B is negative definite, then B−1−A−1 is negative definite and...