Creating an equation library (Updated 03-FEB-2017)
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11-14-2015, 02:50 AM
(This post was last modified: 11-14-2015 02:50 AM by Han.)
Post: #41
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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, 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. Graph 3D | QPI | SolveSys |
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