```python
from sympy import *
init_printing()
#from IPython.display import display
```


```python
th,x,y = symbols('theta,x,y')

display(th)
```


```python
Rth = Matrix([[cos(th),-sin(th)],[sin(th), cos(th)]])

simplify(Rth*Rth.T)
```


```python
X = Matrix([x,y])   # <--- this is a vector

Rth*X
```


```python
simplify((X.T*Rth.T)*(Rth*X))
```


```python
simplify((X.T*Rth.T)*(Rth*X))
```


```python

```

65aa81f79fab37fbcfa5b9997f017e34d654a3e5
ipynb
Jupyter Notebook
teaching/PHY1110/DS/Code/DS09/DS09_A_Orthogonal_Matrices.ipynb
dpcherian/dpcherian.github.io
6110da8c20e05edc106882db8b1c3795ade37708
MIT
teaching/PHY1110/DS/Code/DS09/DS09_A_Orthogonal_Matrices.ipynb
dpcherian/dpcherian.github.io
6110da8c20e05edc106882db8b1c3795ade37708
MIT
teaching/PHY1110/DS/Code/DS09/DS09_A_Orthogonal_Matrices.ipynb
dpcherian/dpcherian.github.io
6110da8c20e05edc106882db8b1c3795ade37708
MIT
Qwen/Qwen-72B
1. YES
2. YES