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  2. Leavitt path algebra - Wikipedia

    en.wikipedia.org/wiki/Leavitt_path_algebra

    Let be a graph satisfying Condition (L), and let () be the associated Leavitt path algebra. If A {\displaystyle A} is a K {\displaystyle K} -algebra and ϕ : L K ( E ) → A {\displaystyle \phi :L_{K}(E)\to A} is an algebra homomorphism with ϕ ( p v ) ≠ 0 {\displaystyle \phi (p_{v})\neq 0} for all v ∈ E 0 {\displaystyle v\in E^{0}} , then ...

  3. Quadrant (plane geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadrant_(plane_geometry)

    Signs of trigonometric functions in each quadrant. In the above graphic, the words in quotation marks are a mnemonic for remembering which three trigonometric functions (sine, cosine, tangent and their reciprocals) are positive in each quadrant. The expression reads "All Science Teachers Crazy" and proceeding counterclockwise from the upper ...

  4. Commutative diagram - Wikipedia

    en.wikipedia.org/wiki/Commutative_diagram

    As a simple example, the diagram of a single object with an endomorphism (:), or with two parallel arrows (, that is, ,:, sometimes called the free quiver), as used in the definition of equalizer need not commute. Further, diagrams may be messy or impossible to draw, when the number of objects or morphisms is large (or even infinite).

  5. Algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry

    Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.

  6. Graph of a function - Wikipedia

    en.wikipedia.org/wiki/Graph_of_a_function

    Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.

  7. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function.

  8. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.

  9. Algebraic graph theory - Wikipedia

    en.wikipedia.org/wiki/Algebraic_graph_theory

    For the Petersen graph, for example, the spectrum of the adjacency matrix is (−2, −2, −2, −2, 1, 1, 1, 1, 1, 3). Several theorems relate properties of the spectrum to other graph properties. As a simple example, a connected graph with diameter D will have at least D+1 distinct values in its spectrum. [1]

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