Lessons Introductory to the Modern Higher Algebra
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In our eReader you can find the full English version of the book. Read Lessons Introductory to the Modern Higher Algebra Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Lessons Introductory to the Modern Higher Algebra
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+ rfy, dx + ey 0, ca; + d|y, dx + ey^ ex+Jy which, dividing both sides of the equation by y^, gives the identity required.
167. We have still to mention another way of forming the canonizant. Let this sought covariant be [A^ B^ (7, D\x^ y)', where we want to determine -4, B^ C^ D) then (Art. 136) {A^ Bj Gj D\j- J — V-) will also yield a covariant. But if this operation is applied to (ic-fX-y)" where a; + \y is a factor in (-4, B^ (7, D\x^ yYy the result must vanish, since one of the factors in ...the operating symbol is ^ \ -y . Since, then, the given quantic is by hypothesis the sum of three terms of the form {x -I- Xy)"*, the result of applying to the given quantic the operating symbol just written must vanish. Thus, then, we have -4 (rf, ejjjxj yY - B (c, d^ ejx^ yY + C (5, c, djx, yY -i>(a, 5,cXa7,y)" = 0, or, equating separately to the coefficients of a?', a?y, y', we have Ad-Bc-^Gb-Da^O^ Ae''Bd+Gc'-Db = Oy Af-Be-hGd-Dc^O^ whence (Art. 28) A is proportional to the determinant got by a, bj c suppressing the column A or 5, c, d c, a, e and so for jB, C, -D, 140 CANONICAL FOEMS.
What to read after Lessons Introductory to the Modern Higher Algebra?
You can find similar books in the "Read Also" column, or choose other free books by George Salmon to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
+ rfy, dx + ey 0, ca; + d|y, dx + ey^ ex+Jy which, dividing both sides of the equation by y^, gives the identity required.
167. We have still to mention another way of forming the canonizant. Let this sought covariant be [A^ B^ (7, D\x^ y)', where we want to determine -4, B^ C^ D) then (Art. 136) {A^ Bj Gj D\j- J — V-) will also yield a covariant. But if this operation is applied to (ic-fX-y)" where a; + \y is a factor in (-4, B^ (7, D\x^ yYy the result must vanish, since one of the factors in ...the operating symbol is ^ \ -y . Since, then, the given quantic is by hypothesis the sum of three terms of the form {x -I- Xy)"*, the result of applying to the given quantic the operating symbol just written must vanish. Thus, then, we have -4 (rf, ejjjxj yY - B (c, d^ ejx^ yY + C (5, c, djx, yY -i>(a, 5,cXa7,y)" = 0, or, equating separately to the coefficients of a?', a?y, y', we have Ad-Bc-^Gb-Da^O^ Ae''Bd+Gc'-Db = Oy Af-Be-hGd-Dc^O^ whence (Art. 28) A is proportional to the determinant got by a, bj c suppressing the column A or 5, c, d c, a, e and so for jB, C, -D, 140 CANONICAL FOEMS.
What to read after Lessons Introductory to the Modern Higher Algebra?
You can find similar books in the "Read Also" column, or choose other free books by George Salmon to read onlineMoreLess
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