| 单词 | singular solution |
| 释义 | > as lemmassingular solution c. Mathematics. (See quots.) singular matrix (see quots. 1964, 1972); singular solution, a solution of a differential equation that cannot be obtained directly from the complete primitive; esp. a solution whose graph is the envelope of the graphs of the complete primitive. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > equation > solution to singular solutiona1832 complementary function1841 solution set1959 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > array > matrix matrix1850 unit matrix1861 adjugate1882 adjoint1889 submatrix1903 identity matrix1908 row matrix1936 transpose1937 singular matrix1964 a1832 A. De Morgan Theory Probab. in Encycl. Metrop. (1845) II. 370/1 There is..what we may call a singular solution for every particular form of θ, which deserves the attention of mathematicians. 1836 A. De Morgan Differential & Integral Calculus xi. 191 If there be a singular solution it is y = a... We have only found the singular solution from the primitive itself. 1859 G. Salmon Lessons Mod. Higher Algebra 45 We shall call those values which make all the differentials vanish, the singular roots of the quantic. 1867 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) III. 461/2 A singular solution of a differential equation..is a function of x and y [etc.]. 1867 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) III. 462/1 The discovery of such solutions depends upon that of singular integrals of the differential equation under consideration. 1869 A. Cayley Coll. Math. Papers VII. 244 Certain forms of the singular curve. 1873 A. Cayley in Messenger of Math. II. 12 I consider the singular solution to be that given by the equation which belongs to the envelope-locus (viz. I do not recognise any singular solution which is not of the envelope species). 1886 A. Cayley Coll. Math. Papers XII. 395 The point x = a is in this case said to be a singular point in regard to the differential equation. 1957 L. Fox Numerical Solution Two-point Boundary Probl. i. 2 The most general solution of an ordinary differential equation of order n contains n arbitrary constants. This general solution is called the Complete Primitive, and a Particular Integral is obtained by giving specific values to these arbitrary constants. Non-linear equations may also have singular solutions, not obtainable from the complete primitive. 1964 N. N. Hancock Matrix Anal. Electr. Machinery ii. 18 A ‘singular’ matrix is one for which the determinant formed by the same array is of zero value. 1972 A. G. Howson Handbk. Terms Algebra & Anal. viii. 43 If there is no matrix B..such that AB = BA = I, then A is said to be singular. < as lemmas |
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