An Elementary Treatise on Determinants: With Their Application to Simultaneous Linear Equations and Algebraical Geometry, Volume 13 |
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1st row a b c def a₁ a₁—b₁ absolute magnitude adjugate Block Algebraical quantities arbitrary values assigned B-Block evanescent B₁ B₂ Block be represented Block formed Block is evanescent Block of 9 C₁ C₂ Cartesian System 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 n-1 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 number of derangements number similar oblong Block Planes intersect Points lie Q. E. D. COROLLARY Q. E. D. PROPOSITION Quadriplanar System real Line 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 Y₁
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Page i - 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. Small 4to. cloth.
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 ii - By T. Combe, MA, EB Gardner, EP Hall, and H. Latham, MA, Printers to the University.
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 120 - Block itself, it may be re-arranged as has been already mentioned; but this cannot be done when they occur in any one of the derived Blocks; in such a case the given Block must be rearranged as circumstances require, and the operation commenced anew. The best way of doing this is as follows :— Suppose a cipher to occur in the...
Page 118 - 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 ]ye found to justify their introduction, as the only way of avoiding tedious periphrasis.
Page 119 - —1 rows and n— 1 columns. (3) Condense this second Block in the same manner, dividing each term, when found, by the corresponding term in the interior of the first Block. (4) Repeat this process as often as may be necessary (observing that in condensing any Block of the series, the...
Page 8 - iJ the row, and the second the column, to which the Element belongs. Thus...
Page 126 - Block of the new series; 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.