Search results
Results from the WOW.Com Content Network
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A Euclidean vector is frequently represented by a directed line ...
A vector field is an assignment of a vector to each point in a space. [1] A vector field in the plane, for instance, can be visualized as a collection of arrows with a given magnitude and direction each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout ...
Initialization vector. In cryptography, an initialization vector ( IV) or starting variable [1] is an input to a cryptographic primitive being used to provide the initial state. The IV is typically required to be random or pseudorandom, but sometimes an IV only needs to be unpredictable or unique. Randomization is crucial for some encryption ...
The following are important identities in vector algebra. Identities that involve the magnitude of a vector , or the dot product (scalar product) of two vectors A · B, apply to vectors in any dimension. Identities that use the cross product (vector product) A × B are defined only in three dimensions. [nb 1] [1] Most of these relations can be ...
The Pre-Advanced Placement pathway for math helps prepare students for further Advanced Placement classes and exams. Purpose. According to the College Board: An AP course in calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities.
A vector space is finite-dimensional if its dimension is a natural number. Otherwise, it is infinite-dimensional, and its dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces occur in many areas of mathematics.
For example, in a fixed basis, a standard linear map that maps a vector to a vector, is represented by a matrix (a 2-dimensional array), and therefore is a 2nd-order tensor. A simple vector can be represented as a 1-dimensional array, and is therefore a 1st-order tensor. Scalars are simple numbers and are thus 0th-order tensors.
Euclidean vector. A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.