| 单词 | positive definite |
| 释义 | > as lemmaspositive definite positive definite adj. Mathematics (of a function) having positive (formerly, positive or zero) values for all non-zero values of its argument; (of a square matrix) having all its eigenvalues positive; (more widely, of an operator on a Hilbert space) such that the inner product of any element of the space with its image under the operator is greater than zero. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of array > relating to matrices > qualities adjoint1856 transposed1858 adjugate1867 orthogonal1891 alternant1892 positive definite1904 skew-symmetric1911 skew-symmetrical1911 unipotent1921 Hermitian1927 non-Hermitian1930 1904 Trans. Amer. Math. Soc. 5 464 It is well known that there is always one such invariant, a positive-definite Hermitian form. 1948 W. V. Houston Princ. Math. Physics (ed. 2) vii. 120 The potential energy will be a quadratic expression in the coordinates that, if the equilibrium is stable, will be a positive definite expression. 1957 L. Fox Numerical Solution Two-point Boundary Probl. vii. 179 If all the λτ are positive, which is the case in many physical problems, and corresponds to some structure of the differential system corresponding to a positive-definite matrix A.., we can also assert [etc.]. 1990 IMA Jrnl. Numerical Anal. 10 546 Hk is a positive definite matrix that approximates the inverse reduced Hessian matrix. < as lemmas |
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