**[1]** Although there is a specialized matrix data type defined in NumPy, it’s more standard to work with ordinary NumPy arrays.\n",
"See [this discussion](https://python-programming.quantecon.org/numpy.html#matrix-multiplication).\n",
"\n",
"

**[2]** Suppose that $ \\|S \\| < 1 $. Take any nonzero vector $ x $, and let $ r := \\|x\\| $. We have $ \\| Sx \\| = r \\| S (x/r) \\| \\leq r \\| S \\| < r = \\| x\\| $. Hence every point is pulled towards the origin."
]
}
],
"metadata": {
"date": 1680677902.2167087,
"filename": "linear_algebra.md",
"kernelspec": {
"display_name": "Python",
"language": "python3",
"name": "python3"
},
"title": "Linear Algebra"
},
"nbformat": 4,
"nbformat_minor": 5
}