Ε-quadratic formIn mathematics, specifically the theory of quadratic forms, an ε-quadratic form is a generalization of quadratic forms to skew-symmetric settings and to *-rings; ε = ±1, accordingly for symmetric or skew-symmetric. They are also called -quadratic forms, particularly in the context of surgery theory. There is the related notion of ε-symmetric forms, which generalizes symmetric forms, skew-symmetric forms (= symplectic forms), Hermitian forms, and skew-Hermitian forms.
Binary quadratic formIn mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables where a, b, c are the coefficients. When the coefficients can be arbitrary complex numbers, most results are not specific to the case of two variables, so they are described in quadratic form. A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms.
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Opera (web browser)Opera is a multi-platform web browser developed by its namesake company Opera. The browser is based on Chromium, but distinguishes itself from other Chromium-based browsers (Chrome, Edge, etc.) through its user interface and other features. Opera was initially released on 10 April 1995, making it one of the oldest desktop web browsers still actively developed. It was commercial software for its first ten years and had its own proprietary layout engine, Presto. In 2013, it switched from the Presto engine to Chromium.
Chromium (web browser)Chromium is a free and open-source web browser project, mainly developed and maintained by Google. This codebase provides the vast majority of code for the Google Chrome browser, which is proprietary software and has some additional features. Chromium's logo is identical in shape to that of Google Chrome, but with blue colors instead of being multicolor. The Chromium codebase is widely used. Microsoft Edge, Samsung Internet, Opera, and many other browsers are based on the Chromium code.
