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    Vector

    Illustration

    Illustration

    Basic definitions

    In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. In topology, a vector is an element of a vector space.

    Detailed definition

    A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and can be specified as (A_1, A_2, ..., A_n). Vectors are sometimes referred to by the number of coordinates they have, so a 2-dimensional vector (x_1, x_2) is often called a two-vector, an n-dimensional vector is often called an n-vector, and so on.

    Related terms

    column vector | contravariant vector | covariant vector | direction | four-vector | head | Helmholtz's theorem | list | n-tuple | null vector | n-vector | one-form | phasor | polar vector | pseudovector | row vector | scalar | tail | tensor | unit vector | vector addition | vector basis | vector bundle | vector difference | vector field | vector function | vector magnitude | vector norm | vector space | vector subtraction | vector sum | zero vector

    Educational grade level

    high school level (California linear algebra standard)

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