A Manual of Quaternions
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In our eReader you can find the full English version of the book. Read A Manual of Quaternions 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 Manual of Quaternions
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68. It happens not imfrequently to be necessary to discriminate between the parts o£ yp^, X' ^^^ ^^ ^h® invariants which arise from the self-conjugate part of (p and those which depend on e. We have yj^YXfx = V(# - Ve)X(* - V6)m = ^VX^x - V . VeX . $M - V#XVeM + V . VeX Ve/x - '^ = ^VX/z + XSe^/x - /xSe^X - eSeX/x, the terms — eSX^yu + eS/x$X cancelling. J. Q. G 98 LINEAR VECTOR FUNCTION. [chap. Viii.
This easily reduces to \lrp = ^p-y^ep-€Sep, (I. ) Thus the spin-vector of i/r is — $e or — (pe.... Operating by or $ + Ve we have mp = Mp-{- Ye^/o - ^Y^ep - YeY^ep - $eSep, and if we notice that ^Y^ep = Ye^p (Ex. 7, Art. 65), this reduces without trouble to m = if— Se#6 or M=m-\-S€^€ (ii. ) where M is an invariant of $. Changing (p into + c, and therefore m into m-{-w/c+rri'c'^-{'C^, $ into #-fc and M into M+Mc + M'^c^ + c^, we see by (ii. ) that wf = M'-e^ or Jf' = m' + e2 and that M"=^m'' (iii. ) Art. 69. We shall give a few examples of the geometrical meaning of the invariants of a linear vector function.
What to read after A Manual of Quaternions?
You can find similar books in the "Read Also" column, or choose other free books by Charles Jasper Joly to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
68. It happens not imfrequently to be necessary to discriminate between the parts o£ yp^, X' ^^^ ^^ ^h® invariants which arise from the self-conjugate part of (p and those which depend on e. We have yj^YXfx = V(# - Ve)X(* - V6)m = ^VX^x - V . VeX . $M - V#XVeM + V . VeX Ve/x - '^ = ^VX/z + XSe^/x - /xSe^X - eSeX/x, the terms — eSX^yu + eS/x$X cancelling. J. Q. G 98 LINEAR VECTOR FUNCTION. [chap. Viii.
This easily reduces to \lrp = ^p-y^ep-€Sep, (I. ) Thus the spin-vector of i/r is — $e or — (pe.... Operating by or $ + Ve we have mp = Mp-{- Ye^/o - ^Y^ep - YeY^ep - $eSep, and if we notice that ^Y^ep = Ye^p (Ex. 7, Art. 65), this reduces without trouble to m = if— Se#6 or M=m-\-S€^€ (ii. ) where M is an invariant of $. Changing (p into + c, and therefore m into m-{-w/c+rri'c'^-{'C^, $ into #-fc and M into M+Mc + M'^c^ + c^, we see by (ii. ) that wf = M'-e^ or Jf' = m' + e2 and that M"=^m'' (iii. ) Art. 69. We shall give a few examples of the geometrical meaning of the invariants of a linear vector function.
What to read after A Manual of Quaternions?
You can find similar books in the "Read Also" column, or choose other free books by Charles Jasper Joly to read onlineMoreLess
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