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Jun
12
asked Solid angle definition - can it be seen shown using an image?
Jun
7
asked Is it possible for an operator to have only one eigenvalue in this case? - in need of a proof
Jun
6
accepted When does exponential function $e^x$ equal $1$?
Jun
6
comment When does exponential function $e^x$ equal $1$?
As i ve thought an Euler identity :)
Jun
6
asked When does exponential function $e^x$ equal $1$?
May
26
comment Inner product vs scalar rpoduct
Well thats how they taught us in schools.
May
26
comment Inner product vs scalar rpoduct
Thanks on the note!
May
26
revised Inner product vs scalar rpoduct
added 22 characters in body
May
26
asked Inner product vs scalar rpoduct
May
20
comment inner product (real or imaginary?)
I forgot to mention i need info for $\mathbb{C}$.
May
20
asked inner product (real or imaginary?)
May
18
accepted Complex 3-D Euclidean space - inner product
May
18
accepted Inner product justification with an example
May
18
comment Weird Identities with Scalar Product & Transpose: $\vec{a}\cdot\vec{b} = \vec{b}^T \cdot {a}^T$, $\vec{a}^T \cdot \vec{b} = \vec{b}^T \cdot \vec{a} $?
I found this later: en.wikipedia.org/wiki/Column_vector It explains well what you have been stating here all along
May
13
comment Inner product justification with an example
I forgot to say that inner product $v\cdot \overline{d}$ isn't demanded to be $\mathbb{C}$, so there isn't any problem here anymore. Is my thinking mathematically correct?
May
13
comment Inner product justification with an example
I am trying to think that an inner product can only be aplied to vectors so first i need a complex vector. And i try to think of a complex vector as a column matrix with complex numbers (at least one has to be ) like this one: $$\vec{v} = \begin{pmatrix}1+3i\\2-i\\ 3\end{pmatrix}$$ and here complex numbers are $v_1=1+3i,\, v_2=2-i,\,v_3 = 3$. So now i can use theese to calculate inner product $v\cdot \overline{v} = v_1\overline{v_1}+v_2\overline{v_2}+v_3\overline{v_3}$ which is always real (and this is what we wanted it to be so now i understand why this definition is OK).
May
13
accepted Weird Identities with Scalar Product & Transpose: $\vec{a}\cdot\vec{b} = \vec{b}^T \cdot {a}^T$, $\vec{a}^T \cdot \vec{b} = \vec{b}^T \cdot \vec{a} $?
May
13
comment Inner product justification with an example
I get $u \cdot u = 2i$ if i calculate it like a dot product and i get $u \cdot u = 2$ if i calculate it as a inner product. Then for $v$ i got $v\cdot v = 0$ if i calculated it as a dot product and $v\cdot v = 3$ if i calculated it as an inner product. Is this good justification for using definition for inner product as it is?
May
13
comment Inner product justification with an example
Thank you. Is there any good case for 3-D vectors describing this? I need 2 different 3-D vectors and a proof of this on them.
May
13
asked Inner product justification with an example