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32 relations: Algebra, Analytic function, Annales de l'Institut Fourier, Basis (linear algebra), Bilinear form, Commutative algebra, Complex number, Complexification, Coordinate system, David Eisenbud, Determinant, Differential topology, Eigenvalues and eigenvectors, Equivalence class, Function (mathematics), Germ (mathematics), Harold Levine, Ideal (ring theory), Jacobian matrix and determinant, Local ring, Modular arithmetic, Neighbourhood (mathematics), Poincaré–Hopf theorem, Polar coordinate system, Quadratic form, Quotient ring, Real coordinate space, Real-valued function, Ring (mathematics), Singularity theory, Topological degree theory, Vector field.
Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Annales de l'Institut Fourier
The Annales de l'Institut Fourier is a French mathematical journal publishing papers in all fields of mathematics.
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Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
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Bilinear form
In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.
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Commutative algebra
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Complexification
In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers.
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Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
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David Eisenbud
David Eisenbud (born 8 April 1947 in New York City) is an American mathematician.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Germ (mathematics)
In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind which captures their shared local properties.
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Harold Levine
Harold I. Levine was an American mathematician who was professor at Stanford University.
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Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Local ring
In abstract algebra, more specifically ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields examined at a particular place, or prime.
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Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
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Poincaré–Hopf theorem
In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology.
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Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
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Quotient ring
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient groups of group theory and the quotient spaces of linear algebra.
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Real coordinate space
In mathematics, real coordinate space of dimensions, written R (also written with blackboard bold) is a coordinate space that allows several (''n'') real variables to be treated as a single variable.
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Real-valued function
In mathematics, a real-valued function is a function whose values are real numbers.
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Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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Singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite.
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Topological degree theory
In mathematics, topological degree theory is a generalization of the winding number of a curve in the complex plane.
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Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
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References
[1] https://en.wikipedia.org/wiki/Eisenbud–Levine–Khimshiashvili_signature_formula
