Faster access than browser!
74 relations: Absolute value, Antisymmetric tensor, Cartesian coordinate system, Coordinate system, Covariance and contravariance of vectors, Cross product, Curl (mathematics), Curvilinear coordinates, Cyclic permutation, Determinant, Differential geometry, Dimension, Einstein notation, Empty product, Epsilon, Euclidean space, Euclidean vector, Factorial, Four-dimensional space, Function (mathematics), Gradient, Gravitation (book), Greek alphabet, Hodge star operator, Index notation, Italians, Jacobian matrix and determinant, Kronecker delta, Latin alphabet, Linear algebra, Linear map, List of permutation topics, Manifold, Mathematician, Mathematics, Metric signature, Metric tensor, Minkowski space, Natural number, Non-Euclidean geometry, Open set, Orthogonal matrix, Orthonormal basis, Parity of a permutation, Permutation, Physicist, Position (vector), Pseudo-Riemannian manifold, Pseudotensor, Pseudovector, ..., Raising and lowering indices, Reflection (mathematics), Ricci calculus, Sign function, Skew-symmetric matrix, Spacetime, Special relativity, Spinor, Square matrix, Supersymmetry, Symmetric tensor, Tensor, Tensor contraction, Tensor density, Tensor field, Three-dimensional space, Time complexity, Transformation matrix, Triple product, Tullio Levi-Civita, Twistor theory, Two-dimensional space, Vector space, Volume form. Expand index (24 more) »
Absolute value
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
New!!: Levi-Civita symbol and Absolute value · See more »
Antisymmetric tensor
In mathematics and theoretical physics, a tensor is antisymmetric on (or with respect to) an index subset if it alternates sign (+/−) when any two indices of the subset are interchanged.
New!!: Levi-Civita symbol and Antisymmetric tensor · See more »
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
New!!: Levi-Civita symbol and Cartesian coordinate system · See more »
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.
New!!: Levi-Civita symbol and Coordinate system · See more »
Covariance and contravariance of vectors
In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.
New!!: Levi-Civita symbol and Covariance and contravariance of vectors · See more »
Cross product
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
New!!: Levi-Civita symbol and Cross product · See more »
Curl (mathematics)
In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.
New!!: Levi-Civita symbol and Curl (mathematics) · See more »
Curvilinear coordinates
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.
New!!: Levi-Civita symbol and Curvilinear coordinates · See more »
Cyclic permutation
In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing (that is, mapping to themselves) all other elements of X. If S has k elements, the cycle is called a k-cycle.
New!!: Levi-Civita symbol and Cyclic permutation · See more »
Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
New!!: Levi-Civita symbol and Determinant · See more »
Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
New!!: Levi-Civita symbol and Differential geometry · See more »
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
New!!: Levi-Civita symbol and Dimension · See more »
Einstein notation
In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.
New!!: Levi-Civita symbol and Einstein notation · See more »
Empty product
In mathematics, an empty product, or nullary product, is the result of multiplying no factors.
New!!: Levi-Civita symbol and Empty product · See more »
Epsilon
Epsilon (uppercase Ε, lowercase ε or lunate ϵ; έψιλον) is the fifth letter of the Greek alphabet, corresponding phonetically to a mid<!-- not close-mid, see Arvanti (1999) - Illustrations of the IPA: Modern Greek. --> front unrounded vowel.
New!!: Levi-Civita symbol and Epsilon · See more »
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
New!!: Levi-Civita symbol and Euclidean space · See more »
Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
New!!: Levi-Civita symbol and Euclidean vector · See more »
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
New!!: Levi-Civita symbol and Factorial · See more »
Four-dimensional space
A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.
New!!: Levi-Civita symbol and Four-dimensional space · See more »
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
New!!: Levi-Civita symbol and Function (mathematics) · See more »
Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
New!!: Levi-Civita symbol and Gradient · See more »
Gravitation (book)
Gravitation is a physics book on Einstein's theory of gravity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler and originally published by W. H. Freeman and Company in 1973.
New!!: Levi-Civita symbol and Gravitation (book) · See more »
Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC.
New!!: Levi-Civita symbol and Greek alphabet · See more »
Hodge star operator
In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.
New!!: Levi-Civita symbol and Hodge star operator · See more »
Index notation
In mathematics and computer programming, index notation is used to specify the elements of an array of numbers.
New!!: Levi-Civita symbol and Index notation · See more »
Italians
The Italians (Italiani) are a Latin European ethnic group and nation native to the Italian peninsula.
New!!: Levi-Civita symbol and Italians · See more »
Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
New!!: Levi-Civita symbol and Jacobian matrix and determinant · See more »
Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
New!!: Levi-Civita symbol and Kronecker delta · See more »
Latin alphabet
The Latin alphabet or the Roman alphabet is a writing system originally used by the ancient Romans to write the Latin language.
New!!: Levi-Civita symbol and Latin alphabet · See more »
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
New!!: Levi-Civita symbol and Linear algebra · See more »
Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
New!!: Levi-Civita symbol and Linear map · See more »
List of permutation topics
This is a list of topics on mathematical permutations.
New!!: Levi-Civita symbol and List of permutation topics · See more »
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
New!!: Levi-Civita symbol and Manifold · See more »
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
New!!: Levi-Civita symbol and Mathematician · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Levi-Civita symbol and Mathematics · See more »
Metric signature
The signature of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive and zero eigenvalues of the real symmetric matrix of the metric tensor with respect to a basis.
New!!: Levi-Civita symbol and Metric signature · See more »
Metric tensor
In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.
New!!: Levi-Civita symbol and Metric tensor · See more »
Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.
New!!: Levi-Civita symbol and Minkowski space · See more »
Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
New!!: Levi-Civita symbol and Natural number · See more »
Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
New!!: Levi-Civita symbol and Non-Euclidean geometry · See more »
Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
New!!: Levi-Civita symbol and Open set · See more »
Orthogonal matrix
In linear algebra, an orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. where I is the identity matrix.
New!!: Levi-Civita symbol and Orthogonal matrix · See more »
Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
New!!: Levi-Civita symbol and Orthonormal basis · See more »
Parity of a permutation
In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations.
New!!: Levi-Civita symbol and Parity of a permutation · See more »
Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
New!!: Levi-Civita symbol and Permutation · See more »
Physicist
A physicist is a scientist who has specialized knowledge in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
New!!: Levi-Civita symbol and Physicist · See more »
Position (vector)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.
New!!: Levi-Civita symbol and Position (vector) · See more »
Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
New!!: Levi-Civita symbol and Pseudo-Riemannian manifold · See more »
Pseudotensor
In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation-preserving coordinate transformation, e.g. a proper rotation, but additionally changes sign under an orientation reversing coordinate transformation, e.g., an improper rotation, that is a transformation expressed as a proper rotation followed by reflection.
New!!: Levi-Civita symbol and Pseudotensor · See more »
Pseudovector
In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but in three dimensions gains an additional sign flip under an improper rotation such as a reflection.
New!!: Levi-Civita symbol and Pseudovector · See more »
Raising and lowering indices
In mathematics and mathematical physics, raising and lowering indices are operations on tensors which change their type.
New!!: Levi-Civita symbol and Raising and lowering indices · See more »
Reflection (mathematics)
In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.
New!!: Levi-Civita symbol and Reflection (mathematics) · See more »
Ricci calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields.
New!!: Levi-Civita symbol and Ricci calculus · See more »
Sign function
In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.
New!!: Levi-Civita symbol and Sign function · See more »
Skew-symmetric matrix
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition In terms of the entries of the matrix, if aij denotes the entry in the and; i.e.,, then the skew-symmetric condition is For example, the following matrix is skew-symmetric: 0 & 2 & -1 \\ -2 & 0 & -4 \\ 1 & 4 & 0\end.
New!!: Levi-Civita symbol and Skew-symmetric matrix · See more »
Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
New!!: Levi-Civita symbol and Spacetime · See more »
Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
New!!: Levi-Civita symbol and Special relativity · See more »
Spinor
In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space.
New!!: Levi-Civita symbol and Spinor · See more »
Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
New!!: Levi-Civita symbol and Square matrix · See more »
Supersymmetry
In particle physics, supersymmetry (SUSY) is a theory that proposes a relationship between two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin.
New!!: Levi-Civita symbol and Supersymmetry · See more »
Symmetric tensor
In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: for every permutation σ of the symbols Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies The space of symmetric tensors of order r on a finite-dimensional vector space is naturally isomorphic to the dual of the space of homogeneous polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that of the antisymmetric tensor or alternating form.
New!!: Levi-Civita symbol and Symmetric tensor · See more »
Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
New!!: Levi-Civita symbol and Tensor · See more »
Tensor contraction
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the natural pairing of a finite-dimensional vector space and its dual.
New!!: Levi-Civita symbol and Tensor contraction · See more »
Tensor density
In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept.
New!!: Levi-Civita symbol and Tensor density · See more »
Tensor field
In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).
New!!: Levi-Civita symbol and Tensor field · See more »
Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
New!!: Levi-Civita symbol and Three-dimensional space · See more »
Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
New!!: Levi-Civita symbol and Time complexity · See more »
Transformation matrix
In linear algebra, linear transformations can be represented by matrices.
New!!: Levi-Civita symbol and Transformation matrix · See more »
Triple product
In vector algebra, a branch of mathematics, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.
New!!: Levi-Civita symbol and Triple product · See more »
Tullio Levi-Civita
Tullio Levi-Civita, FRS (29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas.
New!!: Levi-Civita symbol and Tullio Levi-Civita · See more »
Twistor theory
Twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics.
New!!: Levi-Civita symbol and Twistor theory · See more »
Two-dimensional space
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
New!!: Levi-Civita symbol and Two-dimensional space · See more »
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
New!!: Levi-Civita symbol and Vector space · See more »
Volume form
In mathematics, a volume form on a differentiable manifold is a top-dimensional form (i.e., a differential form of top degree).
New!!: Levi-Civita symbol and Volume form · See more »
Redirects here:
Alternating symbol, Antisymmetric symbol, Completely anti-symmetric tensor, Completly anti-symmetric tensor, Epsilon I J K, Epsilon IJK, Epsilon tensor, Levi civita symbol, Levi-Civita Symbol, Levi-Civita density, Levi-Civita permutation symbol, Levi-Civita pseudotensor, Levi-Civita tensor, Levi-civita symbol, Levi–Civita permutation symbol, Permutation symbol, Permutation tensor.
References
[1] https://en.wikipedia.org/wiki/Levi-Civita_symbol
