Re: Bug in all 85 and 86
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Re: Bug in all 85 and 86
The following is from the TI page
http://www.ti.com/calc/docs/faq/85faq012.htm
.........
Dot product - how is it calculated for complex vectors?
The TI-85, 86 takes the conjugate of the first vector when performing a dot
product calculation of complex vectors. An example is:
[(a,b),(c,d)] dot [(e,f), (g,h)]
(a,-b) * (e,f) + (c,-d)* (g,h)
You then multiply the complex numbers like:
[ (a*e - (-b*f)) + (a*f + (-b*e)) i ] + [ (c*g - (-d*h)) + (c*h + (-d*g)) i
]
...........
This explains the sign difference between what the TI-92 and Maple V give
and what the TI-85/86 gives.
The inner product in the above problem would not involve the conjugate and
would be (a,b)*(e,f)+(c,d)*(g,h)
For real entries the two products would be identical.
------------------------------------------------------------------
Ben Sultenfuss <bsultenfuss@sfasu.edu>
Stephen F. Austin State University
Department of Mathematics and Statistics
1936 North Street
PO Box 13040, SFA Station
Nacogdoches, Texas 75962-3040
Phone: Office: 409-468-3805 Home: 409-560-5508
Fax: Office: 409-468-1669 Home: 409-560-0038
----------
> From: Mark Janeba <mjaneba@willamette.edu>
> To: Ben Sultenfuss <bsultenfuss@SFASU.EDU>
> Cc: GRAPH-TI@LISTS.PPP.TI.COM
> Subject: Re: Bug in all 85 and 86
> Date: Sunday, August 31, 1997 21:38
>
> On Sun, 31 Aug 1997, Ben Sultenfuss wrote:
>
> > u := [2 + 3 I, -4 + 6 I, -2]
> > v := [5. + 7.2 I, 2 - 5 I, -5 + 7 I]
> > > dotprod(u,v);
> > 3.6 + 6.6 I
> > dotprod computes the vector dot product using the standard definition
for a
> > vector space over the complex field: sum u[i]*conjugate(v[i]), as i
ranges
> > over the length of u and v.
> > The TI-85/86 agrees with the cross product. What is of concern is that
the
> > TI-85/86 produces 3.6-6.6i (sign difference) for the dot product.
>
> Hmm... the result you report for the '85/86 is the correct value for
> v-dot-u, with the definition you report for the dot product. (I concur
> that this is the common definition). Is TI using some odd syntax here
that
> leads one to confusion about the order of the operands?
>
> Sorry, my '85 is at the office (and I'm not), or I'd check it myself.
> I'll look in the manual tommorrow (yes, sigh, I *will* be preparing for
> another rousing semester all day tommorrow).
>
> Finally, to address the original poster's comment, I've been meaning to
> use a TI-85 in linear algebra for a while; depending on choice of topics,
> matricies and vectors with complex entries can be an issue in the class.
>
> Regards,
>
> Mark Janeba (503)370-6123
> Dept. of Mathematics e-mail: mjaneba@willamette.edu
> Willamette University web page: http://www.willamette.edu/~mjaneba
> Salem, Oregon 97301-3922 USA "Speaking for myself, not the university"
>