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susam.net | ||
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pfzhang.wordpress.com
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| | | | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | |
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www.math3ma.com
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| | | | | [AI summary] The article explains the hierarchy of integral domains in abstract algebra, detailing the relationships and proofs between fields, Euclidean domains, principal ideal domains, and unique factorization domains. | |
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andrea.corbellini.name
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| | | | | [AI summary] A technical blog post explaining elliptic curves over finite fields, covering modular arithmetic, point addition algorithms, cyclic subgroups, and the discrete logarithm problem in the context of cryptography. | |
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nhigham.com
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| | | In many applications a matrix $latex A\in\mathbb{R}^{m\times n}$ has less than full rank, that is, $latex r = \mathrm{rank}(A) < \min(m,n)$. Sometimes, $latex r$ is known, and a full-rank factorization $LATEX A = GH$ with $latex G\in\mathbb{R}^{m \times r}$ and $latex H\in\mathbb{R}^{r \times n}$, both of rank $latex r$, is given-especially when $latex r =... | ||
