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In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .
In linear algebra, a column vector with elements is an matrix [1] consisting of a single column of entries, for example, = [].. Similarly, a row vector is a matrix for some , consisting of a single row of entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)
Since these four row vectors are linearly independent, the row space is 4-dimensional. Moreover, in this case it can be seen that they are all orthogonal to the vector n = [6, −1, 4, −4, 0] ( n is an element of the kernel of J ), so it can be deduced that the row space consists of all vectors in R 5 {\displaystyle \mathbb {R} ^{5}} that are ...
In order to calculate with vectors, the graphical representation may be too cumbersome. Vectors in an n-dimensional Euclidean space can be represented as coordinate vectors in a Cartesian coordinate system. The endpoint of a vector can be identified with an ordered list of n real numbers (n-tuple).
It is common to call these tuples vectors, even in contexts where vector-space operations do not apply. More generally, when some data can be represented naturally by vectors, they are often called vectors even when addition and scalar multiplication of vectors are not valid operations on these data. [disputed – discuss] Here are some examples.
Date/Time Thumbnail Dimensions User Comment; current: 04:00, 4 March 2018: 512 × 195 (508 bytes): Krishnavedala: New version not comprehendible on all browsers. Also, only symbols are needed for demonstration purposes as the details are mentioned in corresponding texts.
For a vector to represent a geometric object, it must be possible to describe how it looks in any other coordinate system. That is to say, the components of the vectors will transform in a certain way in passing from one coordinate system to another. A simple illustrative case is that of a Euclidean vector.
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 February 2025. Computer graphics images defined by points, lines and curves This article is about computer illustration. For other uses, see Vector graphics (disambiguation). Example showing comparison of vector graphics and raster graphics upon magnification Vector graphics are a form of computer ...