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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 Ï• : L K ( E ) → A {\displaystyle \phi :L_{K}(E)\to A} is an algebra homomorphism with Ï• ( p v ) ≠ 0 {\displaystyle \phi (p_{v})\neq 0} for all v ∈ E 0 {\displaystyle v\in E^{0}} , then ...
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 ...
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.
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.
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.
If G is a covering graph of another graph H, then H is a quotient graph of G. The blocks of the corresponding partition are the inverse images of the vertices of H under the covering map. However, covering maps have an additional requirement that is not true more generally of quotients, that the map be a local isomorphism.
In mathematics, a graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz algebras and Cuntz-Krieger algebras, but the class of graph C*-algebras has been shown to also include several other widely studied classes of C*-algebras. As a result, graph C*-algebras ...
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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