Dot product in the complex space bug ?

Dot product in the complex space bug ?

Post by marche » Sun, 14 Dec 2003 00:39:03

I found interesting message on the TI discussion list. One of the
users over there complained about the bug in the dot product function
when applied to the vector in complex space. The example given was:


On the TI89 it produces 2
On the HP49 it prodcues 2i

Initially many (me including) involved in the discussion thought, that
TI has a bug and HP is right. That was reinforced by the outcome of
the Derive and Mathematica which supposedly produce identical to HP

What is interesting, later in the discussion somebody pointed out,
that the dot product when applied to complex spaces requires second
vector to be conjugated. I've checked the web, and in fact in many
respectable math web sites including Wolfram Research this is how the
dot product is "defined" for the complex spaces. That obvioulsy makes
TI answer correct and everybody else (including expensive desktop
application) buggy ! What you guys think about it ? Are there
inconsistent interpretations of the dot product in the math world when
it comes to the complex spaces ? Is traditional definition for the
real space also viable under certain assumptions as a simply another
operator on the complex space that just happen to be named "dot" ?


1. how do i make the dot space dot space that are used in bulletins?

2. Dot Product on Complex Numbers

I found a curious thing while computing the dot product of two
complex numbers.

Suppose I have complex numbers:
a = 2 + 3i
b = 3 + 6i

If I manually compute this, I get: 24 - 3i
However, using dot( a, b ) returns : 24 + 3i

I've tried many different combinations, and in each case, the result
returned from dot is always the complex conjugate of the correct

According to my linear algebra texts, dot product on complex numbers
is computed by:

(a,b) = a1 * conj ( b1 ) + a2 * conj ( b2 )...

however, it appears matlab is using:
(a,b) = conj ( a1 ) * b1 + conj ( a2 ) * b2 ...

Was this the intended behaviour? Is there a reason for this? Or is
this a bug?


3. Dot and Cross products for Complex Numbers

4. matlab bug/feature with Dot product?

5. Dot Product's imaginary component (dot.m)

6. hit space bar get dots don't want dots

7. transfer time complex algorithm to space complex(in TSP example)

8. The dot product and cross product

9. Fastest way to compute dot product (inner product) in Ruby?

10. Discrepancy between dot product and cross product

11. Suddenly my space bar makes dots instead of spaces,

12. space bar adds a dot between word instead of space

13. space bar puts a dot insteed of space

14. Add-Ins in

15. Where to find complex matrix math add-ins for Excel 2003?