complex vector sum, sumproduct, et cetera

[John Denker <jsd av8n com>]

Hi Folks --

Suppose I have three vectors A, B, and C ... or more specifically
A1:A5, B1:B5, and C1:C5.

Suppose I want to calculate (A+B)•C.

I start by adding A to B, as vectors.  That means adding them
component-by-component.  Then I multiply by C, multiplying
component-by-component.  Then I sum over components.

For floats, this is super-easy to do:  
    =sumproduct(A1:A3+B1:B3,C1:C3)                  [1]

However, for complex numbers I don't see how to do it.  The obvious
approach fails several times over. 
  1a) For one thing, the "+" operator cannot be used to form the sum A+B.
  1b) The imsum(...) function cannot be plugged into equation [1] in
   any obvious way.  Specifically, imsum(A1:A5,B1:B5) returns a scalar,
   not the vector sum, i.e. not the component-by-component sum.
  2) There does not seem to be any imsumproduct(...) AFAICT.

I could easily write a function to do the vector sum, component by 
component ... but I have a question.  What should such a function
be called?
 -- Before you answer "imvectorsum" beware that we will want the
  corresponding component-by-component product, and we should *not*
  call that the "vector product" because that means something else.
 -- The best I've come up with so far is imcomsum(...) and imcomproduct(...).

If anybody has any constructive suggestions, please let us know.

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As a related point, suppose I want to multiply A1:A5 by a scalar. For
floats this is easy, but for complex vectors I don't see any easy way
to do it.  In particular, improduct(A1:A5,3) returns a scalar, not the
component-by-component product.

I reckon we can get imcomproduct(...) to handle this case.

=======

As yet another related point, imsumproduct(...) seems easy and non-problematic.

=======

Also:  Given a sumproduct function, one can code the dot product, namely
  =imsumproduct(A1:A5,imconjugate(B1:B5))           [2]

At this point another question arises:  Given the tremendous practical
importance of [2], would it be worth hard-coding this as a built-in
function?

  =imdotproduct(A1:A5,B1:B5)                       [3]

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See also next message.