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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 03:52, 5 April 2009
, 03:52, 5 April 2009→Commentary Note 8.5
Since multiplication by a 2-adic relative term is a logical analogue of matrix multiplication in linear algebra, all of the products that we computed above can be represented in terms of logical matrices and logical vectors.
Since multiplication by a 2-adic relative term is a logical analogue of matrix multiplication in linear algebra, all of the products that we computed above can be represented in terms of logical matrices and logical vectors.
Here are the absolute terms again, followed by their representation as "coefficient tuples", otherwise thought of as "coordinate vectors".
Here are the absolute terms again, followed by their representation as ''coefficient tuples'', otherwise thought of as ''coordinate vectors''.
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{ccrcccccccccccl}
\mathbf{1}
& = & \mathrm{B}
& +\!\!, & \mathrm{C}
& +\!\!, & \mathrm{D}
& +\!\!, & \mathrm{E}
& +\!\!, & \mathrm{I}
& +\!\!, & \mathrm{J}
& +\!\!, & \mathrm{O}
\\[10pt]
& = & (1 & , & 1 & , & 1 & , & 1 & , & 1 & , & 1 & , & 1)
\\[20pt]
\mathrm{b}
& = &
& &
& &
& &
& &
& &
& &
\mathrm{O}
\\[10pt]
& = & (0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 1)
\\[20pt]
\mathrm{m}
& = &
& & \mathrm{C}
& &
& &
& +\!\!, & \mathrm{I}
& +\!\!, & \mathrm{J}
& +\!\!, & \mathrm{O}
\\[10pt]
& = & (0 & , & 1 & , & 0 & , & 0 & , & 1 & , & 1 & , & 1)
\\[20pt]
\mathrm{w}
& = & \mathrm{B}
& &
& +\!\!, & \mathrm{D}
& +\!\!, & \mathrm{E}
& &
& &
& &
\\[10pt]
& = & (1 & , & 0 & , & 1 & , & 1 & , & 0 & , & 0 & , & 0)
\end{array}</math>
|}
Since we are going to be regarding these tuples as ''column vectors'', it is convenient to arrange them into a table of the following form:
Since we are going to be regarding these tuples as "column vectors", it is convenient to arrange them into a table of the following form:
<pre>
<pre>