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Field lines depicting the electric field created by a positive charge (left), negative charge (center), and uncharged object (right). A field line is a graphical visual aid for visualizing vector fields. It consists of an imaginary integral curve which is tangent to the field vector at each point along its length.
The definition, though with the name ’directivity curve’, was used in a 1967 article by Endre Simonyi. [1] This article also defined 'directivity vector' as = + (), where P and Q are the dx/dt and dy/dt differential equations, and i and j are the x and y direction unit vectors.
The index is not defined at any non-singular point (i.e., a point where the vector is non-zero). It is equal to +1 around a source, and more generally equal to (−1) k around a saddle that has k contracting dimensions and n−k expanding dimensions. The index of the vector field as a whole is defined when it has just finitely many zeroes. In ...
In mathematics, the Conway polynomial C p,n for the finite field F p n is a particular irreducible polynomial of degree n over F p that can be used to define a standard representation of F p n as a splitting field of C p,n. Conway polynomials were named after John H. Conway by Richard A. Parker, who was the first to define them and compute ...
Field lines of a vector field v, around the boundary of an open curved surface with infinitesimal line element dl along boundary, and through its interior with dS the infinitesimal surface element and n the unit normal to the surface. Top: Circulation is the line integral of v around a closed loop C. Project v along dl, then sum.
In terms of the underlying linear algebra, a point belongs to a line if the inner product of the vectors representing the point and line is zero. The lines can be classified into three types. On three of the lines the binary triples for the points have the 0 in a constant position: the line 100 (containing the points 001, 010, and 011) has 0 in ...
In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Otherwise it is a definite quadratic form. More explicitly, if q is a quadratic form on a vector space V over F, then a non-zero vector v in V is said to be isotropic if q(v) = 0.
The trace form for a finite degree field extension L/K has non-negative signature for any field ordering of K. [8] The converse, that every Witt equivalence class with non-negative signature contains a trace form, is true for algebraic number fields K. [8] If L/K is an inseparable extension, then the trace form is identically 0. [9]