determinant (determinant)

and n. [= F. déterm in ant = Sp. Pg. It. deter min ante, II. n. 1. That which determines, fixes, defines, or establishes something. However variable the visible antecedents may be, the real determinants - the co-operant factors - are in each case invariant. G. H. Lewes, Probs. of Life and Mind, II. vi. § 93. 2. In old universities, one who, having taken the lowest degree in arts, had been admitted to act as chief respondent in the Lenten disputations. See determination, 12. Two years later, in due course of his academical studies, this Guillelmus Lauder appears among the Determinants in that College [St. Leonard's, in St. Andrews University]; which shows that he had qualified himself for taking his Master's degree. Lauder, Dewtie of Kyngis (E. E. T. S.), Pref., vi. 3. In math . , the sum of all the products which can be formed of a square block of quantities, each product containing as a factor one num ber from each row and one from each column of the block, and each product being affected by the plus or minus sign according as the arrangement of rows from which its factors are IMG:content-2498.png:[blocks in formation] Aby - Aßc + aẞC - abC + aBe - aBy. The different products of which a determinant is the sum are called its elements. The different quantities which are multiplied to form the elements are called the con stituents of the determinant. The oblique line of places from the upper left-hand to the lower right-hand corner is called the principal diagonal. The conjugate line of places is called the secondary diagonal. The square root of the number of constituents is the ordinal number of the order or degree of the determinant. - Adjugate determinant, one each of whose elements is the cofactor of the corresponding term of the determinant to which it is adjugate.- Axisymmetric determinant. Same as symmetric determinant. See below. - Bialar determinant. See bialar. Bordered determinant, a determinant whose matrix is formed from another by adding new rows and columns, especially where a single row and column 1572 nite; clearly defined or definable; particular: as, a determinate quantity of matter. A determinate number of feet. Dryden, E ay on Dram. Poesy. He talks of power, for example, as if the meaning of the word power were as determinate as the meaning of the word circle. Macaulay, Utilitarian Theory of Government. 2. Predetermined; settled; positive: as, a de terminate rule or order. Being delivered by the determinate counsel and foreknowledge of God. Acts ii. 23. 3t. Decisive; conclusive. I' the progre of this busine , Ere a determinate resolution, he (I mean the bishop) did require a respite. 4t. Determined upon; intended. determinative 5. The mental act of deciding or resolving; the fixing or settling of a mental purpose; the act of resolve. For in every voluntary determination there are certain. ly two elements: the consciousne of an energy or effort, and a distinct feeling of satisfaction in making the effort. Maudsley, Body and Will, p. 87. What I affirm is that you have a power of determining to act, a power of freely forming the internal act of de Mivart, Nature and Thought, p. 213. termination to do something. My determinate voyage is mere extravagancy. Shak ., T. N., ii. 1. 51. Fixed in purpose; resolute; determined. Like men disused in a long peace; more determinate to do, than skilful how to do. Sir P. Sidney. There are some curiosities so bold and determinate as to tell the very matter of her prayer. Jer. Taylor , Works (ed. 1835), I. 29. Determinate idea, an idea not vague, but distinguished from every other. Determinate individual, in logic , a Violent impulse is not the same as a firm determination . J. H. Newman , Parochial Sermons, i. 177. 8t. In old med ., the turning or determining point; the crisis. He carefully noted the determination of these maladies. Swan, tr. of Sydenham. metric determinant, one which is symmetric with spect to both diagonals. Characteristic determinant of a matrix, the determinant of a matrix formed from the given matrix by adding the same indeterminate quantity to each constituent of the principal diagonal. Complementary determinant, a determinant related to a partial determinant, to which it is said to be complementary, by having for its constituents all the constituents of the total determinant which belong to rows and columns from neither of which any constituent of the par tial determinant has been taken, the sign of the comple mentary determinant being determined by taking its matrix as it stands in the lower right-hand corner of the matrix of the total determinant, when the matrix of the partial determinant has been brought to the upper left-hand corner, without altering the value of the total determinant. Composite determinant, a sum of determinants whose matrices are obtained by succe ively omitting all the different combinations of n-columns from a rectangular block of quantities having m -rows and mand n-col umns. tinguished from others. Determinate inflorescence, in bot., same as centrifugal inflorescence (which see, under centrifugal).- Determinate judgment (Gr. ὡρισμένον ἀξίωμα), a proposition whose subject is a demonstrative pronoun: a term of Stoical logic. - Determinate prob lem, in geom, and analysis, a problem which admits of one solution only, or at least a certain and finite number of solutions: being thus opposed to an indeterminate problem, which admits of an infinite number of solutions. determinately (de-ter'mi-nat-li), adv. 1. With certainty; precisely; in a definite manner. The principles of religion are determinately true or false. Til lots on. I have inquired much about Dr. Mead, but can't tell you any thing determinately . Walpole, Letters, II. 226. We perceive the distance of visible objects more exactly and determinately with two eyes than one. Reid , Enquiry, vi. § 22. umns. and one column; second minor, a minor formed by erasing two rows and two columns, etc.- N -dimensional determinant of the rth order, a function of rth const it uents, analogous to an ordinary determinant. - Ortho symmetric determinant, one all the constituents of which, having the sum of the ordinal places of the row and column the same, equal. - Partial Same as to deter rede term i nant, one which is symmetrical with reference to both diagonals. Reciprocal determinant, a determinant each constituent of which is the corresponding first minor of the determinant of which it is the reciprocal. - Skew determinant, one in which every constituent of the ith row and ith column is in every case the negative of the one in the jth row and ith column, except on the principal diagonal. Also called gauche determinant. - Skew symmetric determinant, a skew determinant in which all the constituents of the principal diagonal vanish.- Symmetric determinant, one in which the constituent in the ith row and ith column is in every case equal to that in the ith row and ith column. Zero axial determinant, one in which the constituents of the principal diagonal are all zeros. [The name determinant in a narrower sense was introduced by Gau , and was first applied in the present sense by Cauchy.] determinantal (dē-tér'mi-nan-tal), a. [ The existence of a notation for the elements of a deter minantal product and a knowledge of the properties of the elements facilitate very much the investigation of the laws of repeated determinantal multiplication. T. Muir, Bipartite Functions, Trans. Royal Soc. of Edin., [XXXII. 478. IMG:content-2499.png:[blocks in formation] Determinately bent that she would seek all loving means to win Zelmane. Sir P. Sidney, Arcadia. Before the Reformation, not only were early marriages determinately discouraged, but the opportunity for them did not exist. Froude , Sketches, p. 139.