Dimension

[share]

Dimension

- a measurement of something in a particular direction, especially its height, length, or width

- a part or feature or way of considering something

The dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.

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.[1][2]
Thus a line has a dimension of one (1D) because only one coordinate is needed to
specify a point on it – for example, the point at 5 on a number line.

[share]

เพิ่มเติมครับ

https://en.wikipedia.org/wiki/Dimensional_analysis

Definition

The dimension of a physical quantity can be expressed as a product of the basic physical dimensions
such as length, mass and time, each raised to a rational power.

The dimension of a physical quantity is more fundamental than some scale unit
used to express the amount of that physical quantity.

For example, mass is a dimension, while the kilogram is a particular scale unit
chosen to express a quantity of mass.
Except for natural units, the choice of scale is cultural and arbitrary.

[share]

In mathematics,
the dimension of an object is, roughly speaking, the number of degrees of freedom
of a point that moves on this object.

In other words, the dimension is the number of independent parameters or coordinates
that are needed for defining the position of a point that is constrained to be on the object.

The dimension is an intrinsic property of an object, in the sense that it is independent of
the dimension of the space in which the object is or can be embedded.

[share]

Dimensions are the way we see, measure and experience our world,
by using up and down, right to left, back to front, hot and cold, how heavy and how long,
as well as more advanced concepts from mathematics and physics.

One way to define a dimension is to look at the degrees of freedom,
or the way an object can move in a specific space.
There are different concepts or ways where the term dimension is used,
and there are also different definitions.
There is no definition that can satisfy all concepts.

https://simple.wikipedia.org/wiki/Dimension

[share]

In mathematics, the dimension of a vector space V is the cardinality
(i.e. the number of vectors) of a basis of V over its base field.[1]

It is sometimes called Hamel dimension (after Georg Hamel) or
algebraic dimension to distinguish it from other types of dimension.

For every vector space there exists a basis,[a] and all bases of a vector space have equal cardinality;[b]
as a result, the dimension of a vector space is uniquely defined.
We say V is finite-dimensional if the dimension of V is finite, and infinite-dimensional if its dimension is infinite.

https://en.wikipedia.org/wiki/Dimension_(vector_space)

In mathematics, a set B of elements (vectors) in a vector space V is called a basis,
if every element of V may be written in a unique way as a (finite) linear combination of elements of B.
The coefficients of this linear combination are referred to as components or coordinates on B of the vector.
The elements of a basis are called basis vectors.

https://en.wikipedia.org/wiki/Basis_(linear_algebra)