If anyone wants to try things hands-on, I highly recommend the SymPy (in particular the online live shell https://live.sympy.org/ https://live.sympy.org/ ). The

If anyone wants to try things hands-on, I highly recommend the SymPy (in particular the online live shell https://live.sympy.org/ https://live.sympy.org/ ). The `Matrix` class can be used to create matrices (lists of lists of numbers) and vectors (lists of numbers). Here is a clickable link that demos the first example rotation: https://live.sympy.org/?evaluate=A%20%3D%20Matrix(%5B%5B0%2C%20%201%5D%2C%0A%20%20%20%20%20%20%20%20%20%20%20%20%5B-1%2C%200%5D%5D)%0A%23--%0AA%20*%20Matrix(%5B1%2C0%5D)%0A https://live.sympy.org/?evaluate=A%20%3D%20Matrix(%5B%5B0%2C... For more info about SymPy, see section "VI. Linear algebra" in the SymPy tutorial I wrote https://minireference.com/static/tutorials/sympy_tutorial.pdf https://minireference.com/static/tutorials/sympy_tutorial.pd... (also available as notebook https://github.com/minireference/sympytut_notebooks/blob/master/notebooks/Linear-algebra.ipynb https://github.com/minireference/sympytut_notebooks/blob/mas... )