9.34.3 Can you answer these questions?

9.34.3.1 How do I export/import lists with their assigned names?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=291067

I want to write lists of expressions into an output file with names assigned to each list. 
Later I want to import them in a new notebook for further use. 
Example. 
... 
[output-formatting] [output] [save]
 

asked by BabaYaga https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=39475 Score of 1

answered by BabaYaga https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=39475 Score of 0

9.34.3.2 Mathematica's definition of cos(kA) where A is the 1st Pauli spin matrix

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=291046

For a homework assignment I was asked to derive the formula of $e^{ik\sigma_{1}}$ - where $\sigma_{1}$ is the Pauli spin matrix  {{0,1},{1,0}}  - using the Taylor ... 
[matrix] [linear-algebra] [trigonometry]
 

asked by Raketenmensch https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=94651 Score of 3

9.34.3.3 Using Mathematica to find the eigenvectors

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=290947

I would like some clarification about solving for eigenvectors in Mathematica. 
I am looking at the following matrix: 
\begin{equation*} 
L = 
\begin{pmatrix} 
0 & m(1+\frac{kmwr}{\lambda}) \\ 
q(1-kpx)... 
[matrix] [eigenvalues] [wolfram-cloud]
 

asked by Sprog https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=37135 Score of 1