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Creating an equation library (Updated 03-FEB-2017)
11-14-2015, 02:50 AM (This post was last modified: 11-14-2015 02:50 AM by Han.)
Post: #41
RE: Creating an equation library (updated)
(11-14-2015 02:24 AM)Helge Gabert Wrote:  So, in order to obtain the same DOT() result in CAS as in Home,

in CAS only,

one has to call DOT(CONJ([vector_1]),[vector_2]);

with complex elements in vector_1, in order to negate the complex conjugates which otherwise arise. A bug?

Well, the CAS dot product is the "more correct" dot product for both real and complex vectors since the dot product of a vector with itself is generally considered to be the square of the norm of the vector (and this quantity is a real number, not complex). If a vector \( v \) is complex, the only way to guarantee a real-valued inner product of \( v \) with itself is to define
\[ \langle v, v \rangle = v^H \cdot v \]
where \( v^H \) is the Hermitian transpose (conjugate transpose) and \( v \) is assumed to be in "column" form. What I find amusing is that the ABS(v) command works the same in Home or CAS, whether the vector \( v \) is complex or real -- and the result is actually the square root of \( v^H \cdot v \) in the case where \( v \) is complex. I am not sure why the DOT() command in Home does not work the same way as dot() in CAS view.

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RE: Creating an equation library - Han - 01-10-2015, 03:45 AM
RE: Creating an equation library (updated) - Han - 11-14-2015 02:50 AM



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