NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION: "Mathematics of the Discrete
Fourier Transform (DFT), with Audio Applications --- Second
Edition", by Julius
O. Smith III, W3K
Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright ©
2017-09-28 by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University
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Figure 6.7
illustrates the vector difference 
between
and 
.
From the coordinates, we compute 
.
Figure 6.4:Geometric
interpretation a difference vector.
|
|
Note that the difference vector 
may be
drawn from the tip of 
to the tip of 
rather than from the origin to the point 
;
this is a customary practice which emphasizes relationships among
vectors, but the translation in the plot has no effect on the
mathematical definition or properties of the vector. Subtraction,
however, is not commutative.
To ascertain the proper orientation of the difference vector
,
rewrite its definition as 
, and
then it is clear that the vector should be
the sum of vectors and ,
hence the arrowhead is on the correct endpoint.
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