[Numpy-discussion] dot function or dot notation, matrices, arrays?

[Dag Sverre Seljebotn]

Wayne Watson wrote:
> I'm trying to compute the angle between two vectors in three dimensional 
> space. For that, I need to use the "scalar (dot) product" , according to 
> a calculus book (quoting the book) I'm holding in my hands right now. 
> I've used dot() successfully to produce the necessary angle. My program 
> works just fine.
> 
> In the case of the dot(function), one must use np.dev(x.T,x), where x is 
> 1x3.
> 
> I'm not quite sure what your point is about dot()* unless you are 
> thinking in some non-Euclidean fashion. One can form np.dot(a,b) with a 
> and b arrays of 3x4 and 4x2 shape to arrive at a 3x2 array. That's 
> definitely not a scalar. Is there a need for this sort of calculation in 
> non-Euclidean geometry, which I have never dealt with?

There's a difference between 1D and 2D arrays that's important here. For 
a 1D array, np.dot(x.T, x) == np.dot(x, x), since there's only one 
dimension.

NumPy is all about arrays, not matrices and vectors.

Dag Sverre

> 
> *Maybe it's about something else related to it.
> 
> 
> David Goldsmith wrote:
>> np.dot(x.flat, x.flat) _is exactly_ "sum of squares"(x.flat).  Your
>> math education appears to have drawn a distinction between "dot
>> product" and "scalar product," that, when one is talking about
>> Euclidean vectors, just isn't there: in that context, they are one and
>> the same thing.
>>
>> DG
>>
>> On Fri, Dec 18, 2009 at 9:29 PM, Wayne Watson
>> <sierra_mtnview@sbcglobal.net> wrote:
>>   
>>> I'll amend that. I should have said, "Dot's all folks." -- Bugs Bunny
>>>
>>> --
>>>           Wayne Watson (Watson Adventures, Prop., Nevada City, CA)
>>>
>>>             (121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
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>>>
>>>             "... humans'innate skills with numbers isn't much
>>>              better than that of rats and dolphins."
>>>                       -- Stanislas Dehaene, neurosurgeon
>>>
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>>>
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>>   
> 


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Dag Sverre