A Treatise On the Theory of Determinants And Their Applications in Analysis ...
A Treatise On the Theory of Determinants And Their Applications in Analysis ...
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In our eReader you can find the full English version of the book. Read A Treatise On the Theory of Determinants And Their Applications in Analysis ... 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 A Treatise On the Theory of Determinants And Their Applications in Analysis ...
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To quickly assess the difficulty of the text, read a short excerpt:
Next, let us compound two arrays 1, l 19 m v n t 1, -\y -fi lt -if t 1, -*»»-AV -V 1, l 9 , m 9 , n p We get the determinant | l-cos(tfc)| = | 2sin s i(iJfc)| Digitized by Google 11 — 13.] APPLICATIONS TO GEOMETRY.
Hence, by iv. 2, for two sets of five straight. lines . • = 191 (i).
16 sin f £(ll)...sin 9 £(15) sin*£(51)...sin*£(55) For two sets of four straight lines a, 6, c, d ; a, b\ c\ d', = -|l, ?«,*»«, n, | x|l, \ 9 fi it p t \ (i=l,2,3,4) (ii).
sin* | (aa) . . , sin*£ {ad') sin , i(da')......8in , i(c«') Expanding the determinants on the right according to the elements of their first column, our determinant = {sin (bed) + sin (cad) + sin (abd) — sin (abc)} x {sin [Vc'd') + sin (c'a'd') + sin (a'b'd') - sin (a'&V)}.
For two sets of three straight lines, our determinant is 1- cos (11) ... 1- cos (13) | 1- cos (31) ... 1 -cos (33); or 1, ...
1, 1- cos (11)... 1- cos (13) 1, 1, 1- cos (31),.. 1- cos (33) 1, -1, 1, -cos (11) 1, 1, -cos (31) ... -cos (33) -1 - cos (13) This is equal to the sum ot the products of determinants of the third order taken from the two arrays.
What to read after A Treatise On the Theory of Determinants And Their Applications in Analysis ...?
You can find similar books in the "Read Also" column, or choose other free books by Scott Robert Forsyth to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Next, let us compound two arrays 1, l 19 m v n t 1, -\y -fi lt -if t 1, -*»»-AV -V 1, l 9 , m 9 , n p We get the determinant | l-cos(tfc)| = | 2sin s i(iJfc)| Digitized by Google 11 — 13.] APPLICATIONS TO GEOMETRY.
Hence, by iv. 2, for two sets of five straight. lines . • = 191 (i).
16 sin f £(ll)...sin 9 £(15) sin*£(51)...sin*£(55) For two sets of four straight lines a, 6, c, d ; a, b\ c\ d', = -|l, ?«,*»«, n, | x|l, \ 9 fi it p t \ (i=l,2,3,4) (ii).
sin* | (aa) . . , sin*£ {ad') sin , i(da')......8in , i(c«') Expanding the determinants on the right according to the elements of their first column, our determinant = {sin (bed) + sin (cad) + sin (abd) — sin (abc)} x {sin [Vc'd') + sin (c'a'd') + sin (a'b'd') - sin (a'&V)}.
For two sets of three straight lines, our determinant is 1- cos (11) ... 1- cos (13) | 1- cos (31) ... 1 -cos (33); or 1, ...
1, 1- cos (11)... 1- cos (13) 1, 1, 1- cos (31),.. 1- cos (33) 1, -1, 1, -cos (11) 1, 1, -cos (31) ... -cos (33) -1 - cos (13) This is equal to the sum ot the products of determinants of the third order taken from the two arrays.
What to read after A Treatise On the Theory of Determinants And Their Applications in Analysis ...?
You can find similar books in the "Read Also" column, or choose other free books by Scott Robert Forsyth to read onlineMoreLess
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