Lists of vector identities information

There are two lists of mathematical identities related to vectors: Vector algebra relations — regarding operations on individual vectors such as dot product...

The following are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)}...

The following are important identities in vector algebra. Identities that only involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|}...

identities Summation identities Vector calculus identities List of inequalities List of set identities and relations – Equalities for combinations of...

topics Lists of integrals Lists of shapes Lists of statistics topics Lists of unsolved problems in mathematics Lists of vector identities Lists of animals...

theorem of vector calculus states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational...

these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially...

Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional...

non-zero vector in the same direction as the original. Yet another example of structure without identity element involves the additive semigroup of positive...

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...

This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation...

respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be...

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's...

B_{z}\end{bmatrix}}.} This identity is a coordinate dependent result, and is not general. An example of the usage of the vector Laplacian is the Navier-Stokes...

tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g...

In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...

This mechanism generalizes Vector Clocks and allows operation in dynamic environments when the identities and number of processes in the computation...

curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes...

(that is, a function of position which returns a scalar as a value), or a vector field (that is, a function which returns a vector as value). If a region...

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle...

derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change...

Both works contain many identities concerning specific integrals, which are organized with the most relevant topic instead of being collected into a separate...

{\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } is a function taking as input a vector x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} and outputting...

In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order...

Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type...

to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f ( x , y , … ) {\displaystyle...

facilitate applying identities to expressions that are complicated or use the same symbols as the identity. For example, the identity ( L ∖ M ) ∖ R   =...