Determinants sentence example
This determinant and that associated with Aik are termed corresponding determinants.
Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
Dodgson periodically published mathematical works - An Elementary Treatise on Determinants (1867); Euclid, Book V., proved Algebraically (1874); Euclid and his Modern Rivals (1879), the work on which his reputation as a mathematician largely rests; and Curiosa Mathematica (1888).
The theories of determinants and of symmetric functions and of the algebra of differential operations have an important bearing upon this comparatively new branch of mathematics.
Similarly, by putting one or more of the deleted rows or columns equal to rows or columns which are not deleted, we obtain, with Laplace, a number of identities between products of determinants of complementary orders.Advertisement
Functional determinants were first investigated by Jacobi in a work De Determinantibus Functionalibus.
Linear Equations.-It is of importance to study the application of the theory of determinants to the solution of a system of linear equations.
Cayley, however, has shown that, whatever be the degrees of the three equations, it is possible to represent the resultant as the quotient of two determinants (Salmon, l.c. p. 89).
Every unit of the rth species which does not vanish is the product of r different units of the first species; two such units are independent unless they are permutations of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants.
The germs of the theory of determinants are to be found in the works of Leibnitz; Etienne Bezout utilized them in 1764 for expressing the result obtained by the process of elimination known by his name, and since restated by Arthur Cayley.Advertisement
His name appears in 1477 in the Register of the Faculty of Arts at St Andrews, among the Determinants or Bachelors of Arts, and in 1479 among the masters of the university.
Besides the conventional use of certain signs as the indications of names of gods, countries, cities, vessels, birds, trees, &c., which, known as " determinants," are the Sumerian signs of the terms in question and were added as a guide for the reader, proper names more particularly continued to be written to a large extent in purely " ideographic " fashion.
It was considered by Biot to have been originally twenty-four, but to have been enlarged to twenty-eight about i ioo B.C., by the addition of determinants for the solstices and equinoxes of that period.
Eight junction stars lie quite close to, seven others are actually identical with, Chinese determinants; 14 and many of these coincidences 9 Sir William Jones, As.
Eighteen Chinese determinants were included in the Arab asterisms, and of these five or six were not nakshatra stars; consequently, they must have been taken directly from the Chinese series.Advertisement
As a mathematician he occupied himself with many branches of his favourite science, more especially with higher algebra, including the theory of determinants, with the general calculus of symbols, and with the application of analysis to geometry and mechanics.
To a mind imbued with the love of mathematical symmetry the study of determinants had naturally every attraction.
To this, the first elementary treatise on determinants, much of the rapid development of the subject is due.
The effect of the study on Mr Spottiswoode's own methods was most pronounced; there is scarcely a page of his mathematical writings that does not bristle with determinants."
Given the presence of all the necessary determinants for the development of pigment in a mammal's coat, some or all of the hairs may bear this pigment according to the pattern determinants, or absence of pattern determinants, which the cells of the hair papillae carry.Advertisement
And this leads to the inquiry as to whether albinoes ever exhibit evidence that they carry the pattern determinants in the absence of those for pigmentation.
For it is to be expected a priori that, since albinoes were derived from pigmented progenitors and may at any time appear, side by side with pigmented brothers, in a litter from pigmented parents, they would be carrying the pattern determinants of some one or other of their pigmented ancestors.
With regard to pattern, the evidence is now clear that albinoes may carry the determinants in both these ways.
Not only do albinoes thus carry the determinants for pattern, but it has been known for some time that they also carry gametically, but never visible somatically, the determinants for either the ferment or the chromogen for one or more colours.
C. C. Hurst, more recently, has shown that albino rabbits, whether pure bred for eight generations at least, or extracted from pigmented parents, may carry the determinants for black or for black and grey.Advertisement
In this latter case the determinants for black are carried by separate gametes from those carrying grey, and the two kinds of sex-cells exist in approximately equal numbers.
This is likewise true of albino mice when they carry the determinants for more than one colour.
P. Mudge have both shown that albino rats also carry in a latent condition the determinants for black or grey.
Or, to express it otherwise, an albino extracted from yellow parents, bred with an albino extracted from black parents, will give an albino offspring whose gametes in equal numbers are bearers of the black and yellow determinants.
Some of the individuals will be one or other of the two colours, the determinants of which were borne by the albino, and others the colour of the pigmented parent.
Distance from the ocean, situation with reference to the mountain ranges, and altitude are all important determinants of these climatic differences; but of these the last seems to be most important.
More and.more he learned from Cabanis and Helvetius to see in the will and the passions the determinants of intellectual life, and in the character and the temper the source of theories and beliefs.
For even when the felt obligation is absolute, where the will is completely moralized, where it is inconceivable in the case of a good man that the act which he performs should be other than it is, there the obligation which he recognizes is an obligation to choose autonomously, and as such is distinguished from desire or appetite or any of the other alleged determinants of action.
Moreover, the functions b'c" - b"c', b"c - bc", bc' - b'c used in the process are themselves the determinants of the second order l b",c"I?
I b",c"I I We have herein the suggestion of the rule for the derivation of the determinants of the orders 1, 2, 3, 4, &c., each from the preceding one, viz.
Moreover, representing the remaining three lines by a" b" c" d" e" b /r c a, d N, e"' a " c 'N d"N err" it is further seen that the factor which multiplies the determinant formed with any two columns of the first set is the determinant of the third order formed with the complementary three columns of the second set; and it thus appears that the determinant of the fifth order is a sum of all the products of the form ' a b c" d" e" a, b"c"'dN, ear the sign being in each case such that the sign of the term .c"d"'e" obtained from the diagonal elements of the component determinants may be the actual sign of this term in the determinant of the fifth order; for the product written down the sign is obviously +.
The germ of the theory of determinants is to be found in the writings of Gottfried Wilhelm Leibnitz (1693), who incidentally discovered certain properties when reducing the eliminant of a system of linear equations.
Determinants were also employed by Etienne Bezout in 1764, but the first connected account of these functions was published in 1772 by Charles Auguste Vandermonde.
Laplace developed a theorem of Vandermonde for the expansion of a determinant, and in 1773 Joseph Louis Lagrange, in his memoir on Pyramids, used determinants of the third order, and proved that the square of a determinant was also a determinant.
Although he obtained results now identified with determinants, Lagrange did not discuss these functions systematically.
To Gauss is due the establishment of the important theorem, that the product of two determinants both of the second and third orders is a determinant.
His treatises and contributions to scientific journals (to the number of 789) contain investigations on the theory of series (where he developed with perspicuous skill the notion of convergency), on the theory of numbers and complex quantities, the theory of groups and substitutions, the theory of functions, differential equations and determinants.
Dr. Carlton A Evans Research Overview We are investigating the determinants of TB susceptibility in Peru, focusing on the effects of malnutrition.
Her PhD thesis examines the determinants of the accuracy of analyst earnings forecasts in the UK.
The Sustainable Development Commission welcomes the White Paper and the priority given to reducing health inequalities and tackling the wider determinants of health.
The definition of a determinant in all dimensions will be given in detail, together with applications and techniques for calculating determinants.
The aim of this paper is to identify the main determinants of child health in Bolivia.
We analyze the determinants of graduate first destinations and suggest a method for the construction of university performance indicators.
Unmeasured determinants of employees quot we why would the.
In summary, despite their more favorable position with respect to socioeconomic determinants of health, males have higher mortality rates.
Even in the 1900s, however, thresholds continue to characterize the relationship of education to several of the proximate determinants that reduce fertility.
Observed determinants of prwora with the data are four.
Starter strains had less virulence determinants than food strains, which in turn had less than the pathogenic strains.
In addition to these tissue specificity determinants a core set of basic pathogenicity factors will be generally required for plant colonization.
A number of determinants were considered germane in the selection of mediation for commercial disputes.
Needlesticks, nurses, and organization 2 Clinical bottom line Nurse staffing and organization are key determinants of needlestick risk.
For the subjects of this general heading see the articles ALGEBRA; ALGEBRAIC FORMS; ARITHMETIC; COMBINATORIAL ANALYSIS; DETERMINANTS; EQUATION; FRACTION, CONTINUED; INTERPOLATION; LOGARITHMS; MAGIC SQUARE; PROBABILITY.
Similarly p lines rs of deletion intersecting in p 2 points yield corresponding determinants of orders p and n-p respectively.
He was one of the early founders of the theory of determinants; in particular, he invented the functional determinant formed of the n 2 differential coefficients of n given functions of n independent variables, which now bears his name (Jacobian), and which has played an important part in many analytical investigations (see Algebraic Forms).
Cuenot and Hurst have also shown that when albinoes of one colour extraction are crossed with albinoes of another colour extraction the segregation of the colour determinants in the gametogenesis of the albinoes takes place in precisely the same way that it does in the gametogenesis of a pigmented individual; that is, in Mendelian fashion.
They carry only some determinant or determinants which are capable of developing colour when they interact with some other determinant or determinants carried alone by pigmented individuals.
We are interested in the role that determinants play in determining new solutions to various soliton equations.
Baggley A., et al. "Determinants of women's decision making on whether to treat nausea and vomiting of pregnancy pharmacologically."
This model posits that information, motivation, and behavior are the primary determinants of AIDS-related preventive behavior.
Such determinants are called symmetrical.