An Elementary Treatise on Determinants: With Their Application to Simultaneous Linear Equations and Algebraical Geometry, Volume 13Macmillan and Company, 1867 - 143 pages |
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Common terms and phrases
1st row a₁ absolute magnitude adjugate Block Algebraical Geometry arbitrary values assigned B-Block evanescent B₁ B₂ Block be represented Block formed Block is evanescent Block of 9 C₁ Cartesian System CHAP complemental Minor Constituent contain actually containing n Variables COROLLARY TO PROP D₁ D₂ Elements Equa Equation being aa Equation is dependent Equations are consistent Equations containing Variables finite or infinite given Block Hence inconsistent infinite distance Let the Block Let the test let them contain Line longitudinals multiplied n-1 Equations n-1 Variables non-evanescent Minor non-evanescent principal Minor nth degree number of derangements number similar oblong Block Plane Geometry Planes intersect Points lie Q. E. D. COROLLARY Q. E. D. PROPOSITION Quadriplanar System quantities secondary Minor Secondly set of values square Block symbol systematic Equation test be fulfilled test is necessary Trilinear System V-Block not evanescent vanishes VIII whence
Popular passages
Page i - DodgSOn.— AN ELEMENTARY TREATISE ON DETERMINANTS, with their Application to Simultaneous Linear Equations and Algebraical Geometry. By CHARLES L DODGSON, MA, Student and Mathematical Lecturer of Christ Church, Oxford.
Page ii - By T. Combe, MA, EB Gardner, EP Hall, and H. Latham, MA, Printers to the University.
Page 19 - ... 418. Two proportions being given, we may always produce a new one, by separately multiplying the first term of the one by the first term of the other, the second by the second, and so on, with respect to the other terms. Thus, the proportions a : b = c : d and e :/=£ : h will furnish this, ae : bf= eg : d h.
Page 119 - interior of a Block " to denote the Block which remains when the first and last rows and columns are erased. The process of "Condensation" is exhibited in the following rules, in which the given block is supposed to consist of n rows and n columns : — (1) Arrange the given Block, if necessary, so that no ciphers occur in its interior.
Page 17 - The addition to the elements of any row (or column), the corresponding elements of any other row (or column) multiplied by any number.
Page iii - New words and symbols are always a most unwelcome addition to a Science, especially to one already burdened with an enormous vocabulary, yet I think the Definitions given of them will be found to justify their introduction, as the only way of avoiding tedious periphrasis.
Page 120 - This process cannot be continued when ciphers occur in the interior of any one of the Blocks, since infinite values would be introduced by employing them as divisors. When they occur in the given Block itself, it may be re-arranged...
Page 8 - Minor to each other. the row, and the second the column, to which the Element belongs. Thus, a Block of m rows and n columns may be represented thus : — "i\i,i\2 ...... i\ \ l,m\\ 2 ...... m\ n II.
Page 124 - Block containing n rows and n+1 columns, and 'condense, it, we reduce it at last to 2 terms, the first of which is the Determinant of the first n...
Page 126 - Block of the new series; -5 2 and proceeding thus we ultimately obtain the two terms 12, 12. Observing' that the y-column has the sign + placed over it, we multiply the first 12 by +y, and so form the Equation 12^ = 12, which gives y = 1.