MagicInternetMath on Nostr: 📖 Normal Basis For a normal extension $E/F$ with Galois group $G = \\{\\sigma_1, ...

📖 Normal Basis

For a normal extension $E/F$ with Galois group $G = \\{\\sigma_1, \\ldots, \\sigma_n\\}$, a normal basis is an element $\\theta \\in E$ such that $\\sigma_1(\\theta), \\ldots, \\sigma_n(\\theta)$ are linearly independent over $F$ (and hence form a basis).

From: gal-artin
Learn more: https://mathacademy-cyan.vercel.app/#/section/19

Explore all courses: https://mathacademy-cyan.vercel.app