8.6.2 Greatest hits from previous weeks

8.6.2.1 How do I get the inverse of a homogeneous transformation matrix?
8.6.2.2 Parallel and perpendicular symbol from Mathematica to $\LaTeX$
8.6.2.3 Creating a table/Matrix during a For loop
8.6.2.4 Multivariable Taylor expansion does not work as expected
8.6.2.5 1 Plot, 2 Scale/Axis
8.6.2.6 All that doesn't glitter isn't gold
8.6.2.7 Is there something like DensityPlot3D to visualize atomic orbitals?
8.6.2.1 How do I get the inverse of a homogeneous transformation matrix?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=106257

I want to get the inverse of this homogeneous transformation matrix: 
 
 iab = { 
{1, 0, 0, 0}, 
{0, 0, -1, 0}, 
{0, 1, 0, 3}, 
{0, 0, 0, 1} 
} 
 
 
using the ... 
[matrix] [linear-algebra] [inverse] [geometric-transform] [rotation]
 
asked by andrestoga https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=37677 Score of 5
answered by march https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=29734 Score of 13
8.6.2.2 Parallel and perpendicular symbol from Mathematica to $\LaTeX$

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=46538

I want to get the following expression from Mathematica to $\LaTeX$: 
 
\begin{bmatrix} 
E_{\parallel} \\ E_{\perp} 
\end{bmatrix} 
 
I have tried to use inbuilt 'symbol' character from the special ... 
[latex]
 
asked by Steve Hatcher https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=13314 Score of 20
answered by Sjoerd C. de Vries https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=57 Score of 27
8.6.2.3 Creating a table/Matrix during a For loop

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=2930

I have a  For  loop (with  i  as a counter), which calculates different values ( y1 , ... 
[matrix]
 
asked by Solarboy https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=727 Score of 12
answered by Mr.Wizard https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=121 Score of 15
8.6.2.4 Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows: 
 
$$ 
f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot \nabla)... 
[calculus-and-analysis] [series-expansion]
 
asked by matheorem https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4742 Score of 70
answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 Score of 78
8.6.2.5 1 Plot, 2 Scale/Axis

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=627

I would like to plot those two datasets on top of each other. But they have very different range on the $y$ axis. How can I have two different axis? 
 
I found the following on the help menu but quite ... 
[plotting] [customization]
 
asked by 500 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=172 Score of 156
answered by ArgentoSapiens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=92 Score of 158
8.6.2.6 All that doesn't glitter isn't gold

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=249714

I would like to color some objects in metallic shades like gold and silver. Various web sources suggest that the gold is a variant of yellow with RGB values 83.14% red, 68.63% green, and 21.57% blue. ... 
[graphics] [color]
 
asked by bill s https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1783 Score of 22
8.6.2.7 Is there something like DensityPlot3D to visualize atomic orbitals?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=32378

I'm visualizing some hydrogen like atomic orbitals.  For looking at plane slices of the probability density, the  DensityPlot  function works well, and with something ... 
[plotting] [physics] [chemistry]
 
asked by Peeter Joot https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=10 Score of 45
answered by xslittlegrass https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1364 Score of 25