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Nullity (other)
{{disambiguation ...
Nullity may refer to: * Legal nullity, something without legal significance * Nullity (conflict), a legal declaration that no marriage had ever come into being Mathematics * Nullity (linear algebra), the dimension of the kernel of a mathematical operator or null space of a matrix * Nullity (graph theory), the nullity of the adjacency matrix of a graph * Nullity, the difference between the size and rank of a subset in a matroid * Nullity, a concept in transreal arithmetic denoted by Φ, or similarly in wheel theory denoted by ⊥. See also * Null * Nullification Nullification may refer to: * Nullification (U.S. Constitution), a legal theory that a state has the right to nullify any federal law deemed unconstitutional with respect to the United States Constitution ** Nullification crisis, the 1832 confron ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legal Nullity
Legal nullity refers to any entity which theoretically is, or might be, of some legal significance, but in fact lacks any identity or distinct structure of its own. Institutional bodies The usual examples are counties (or equivalent sub-regional groupings) which are wholly subsumed by the municipal government within their boundaries.Textbook on Legal Language and Legal Writing Bhatia, K, L. 2010. Universal Law Publishing. p269. Retrieved: 27/05/18 Some entities which fit this description are , a legal nullity because it is entirely coterminous with the city of |
Nullity (conflict)
Conflict of marriage laws is the conflict of laws with respect to marriage in different jurisdictions. When marriage-related issues arise between couples with diverse backgrounds, questions as to which legal systems and norms should be applied to the relationship naturally follow with various potentially applicable systems frequently conflicting with one another. The choice of law The standard choice of law rules for adjudicating on issues relating to marriage represent a balance between the various public policies of the laws involved: Status and capacity Status and capacity are defined by the personal laws of the parties, namely: * the '' lex domicilii'' or law of the domicile in common law states, and * either the '' lex patriae'' or law of nationality, or law of habitual residence in civil law states). The personal laws will usually define status in rem so that it is recognised wherever the individual may travel subject only to significant public policy limits. Hen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nullity (linear Algebra)
In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. That is, given a linear map between two vector spaces and , the kernel of is the vector space of all elements of such that , where denotes the zero vector in , or more symbolically: \ker(L) = \left\ = L^(\mathbf). Properties The kernel of is a linear subspace of the domain .Linear algebra, as discussed in this article, is a very well established mathematical discipline for which there are many sources. Almost all of the material in this article can be found in , , and Strang's lectures. In the linear map L : V \to W, two elements of have the same image in if and only if their difference lies in the kernel of , that is, L\left(\mathbf_1\right) = L\left(\mathbf_2\right) \quad \text \quad L\left(\mathbf_1-\mathbf_2\right) = \mathbf. From this, it follows b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel (linear Algebra)
In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. That is, given a linear map between two vector spaces and , the kernel of is the vector space of all elements of such that , where denotes the zero vector in , or more symbolically: \ker(L) = \left\ = L^(\mathbf). Properties The kernel of is a linear subspace of the domain .Linear algebra, as discussed in this article, is a very well established mathematical discipline for which there are many sources. Almost all of the material in this article can be found in , , and Strang's lectures. In the linear map L : V \to W, two elements of have the same image in if and only if their difference lies in the kernel of , that is, L\left(\mathbf_1\right) = L\left(\mathbf_2\right) \quad \text \quad L\left(\mathbf_1-\mathbf_2\right) = \mathbf. From this, it follows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Space
In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. That is, given a linear map between two vector spaces and , the kernel of is the vector space of all elements of such that , where denotes the zero vector in , or more symbolically: \ker(L) = \left\ = L^(\mathbf). Properties The kernel of is a linear subspace of the domain .Linear algebra, as discussed in this article, is a very well established mathematical discipline for which there are many sources. Almost all of the material in this article can be found in , , and Strang's lectures. In the linear map L : V \to W, two elements of have the same image in if and only if their difference lies in the kernel of , that is, L\left(\mathbf_1\right) = L\left(\mathbf_2\right) \quad \text \quad L\left(\mathbf_1-\mathbf_2\right) = \mathbf. From this, it follows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (: matrices) is a rectangle, rectangular array or table of numbers, symbol (formal), symbols, or expression (mathematics), expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " matrix", or a matrix of dimension . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotation (mathematics), rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nullity (graph Theory)
The nullity of a graph in the mathematical subject of graph theory can mean either of two unrelated numbers. If the graph has ''n'' vertices and ''m'' edges, then: * In the matrix theory of graphs, the nullity of the graph is the nullity of the adjacency matrix ''A'' of the graph. The nullity of ''A'' is given by ''n'' − ''r'' where ''r'' is the rank of the adjacency matrix. This nullity equals the multiplicity of the eigenvalue 0 in the spectrum of the adjacency matrix. See Cvetkovič and Gutman (1972), Cheng and Liu (2007), and Gutman and Borovićanin (2011). * In the matroid theory the nullity of the graph is the nullity of the oriented incidence matrix ''M'' associated with the graph. The nullity of ''M'' is given by ''m'' − ''n'' + ''c'', where, ''c'' is the number of components of the graph and ''n'' − ''c'' is the rank of the oriented incidence matrix. This name is rarely used; the number is more commonly known as the cycle rank, cyclomatic number, or circuit rank o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matroid
In combinatorics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid Axiomatic system, axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or ''flats''. In the language of partially ordered sets, a finite simple matroid is equivalent to a geometric lattice. Matroid theory borrows extensively from the terms used in both linear algebra and graph theory, largely because it is the abstraction of various notions of central importance in these fields. Matroids have found applications in geometry, topology, combinatorial optimization, network theory, and coding theory. Definition There are many Cryptomorphism, equivalent ways to define a (finite) matroid. Independent sets In terms of independence, a finite matroid M is a pair (E, \mathcal), where E is a finite set (called the ''gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wheel Theory
A wheel is a type of algebra (in the sense of universal algebra) where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring. The term ''wheel'' is inspired by the topological picture \odot of the real projective line together with an extra point ⊥ (bottom element) such that \bot = 0/0. A wheel can be regarded as the equivalent of a commutative ring (and semiring) where addition and multiplication are not a group but respectively a commutative monoid and a commutative monoid with Involution_(mathematics), involution. Definition A wheel is an algebraic structure (W, 0, 1, +, \cdot, /), in which * W is a set, * 0 and 1 are elements of that set, * + and \cdot are binary operations, * / is a unary operation, and satisfying the following properties: * + and \cdot are each commutative and associative, and have \,0 and 1 as their respective Identity element, identities. * / is an involut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null (other)
Null may refer to: Science, technology, and mathematics Astronomy *Nuller, an optical tool using interferometry to block certain sources of light Computing *Null (SQL) (or NULL), a special marker and keyword in SQL indicating that a data value does not exist, is not known, or is missing. *Null character, the zero-valued ASCII character, also designated by , often used as a terminator, separator or filler. This symbol has no visual representation. *Null device, a virtual file that discards data written to it, on Unix systems /dev/null *Null pointer or reference (sometimes written NULL, nil, or None), an object pointer (or reference) not currently set to point (or refer) to a valid object Mathematics *Null (mathematics), a zero value in several branches of mathematics Physics *Null (physics), a point in a field where the field quantity is zero *Null (radio), a concept in electromagnetism Arts and media *The Null Corporation, an imprint of the band Nine Inch Nails * ''Null'' (Intro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
