n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers, also known as complex vectors. The space is denoted...

Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars...

two-dimensional complex space – such as the two-dimensional complex coordinate space, the complex projective plane, or a complex surface – has two complex dimensions...

mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an...

In mathematics, the real coordinate space or real coordinate n-space, of dimension n, denoted Rn or R n {\displaystyle \mathbb {R} ^{n}} , is the set...

in the complex coordinate space C n {\displaystyle \mathbb {C} ^{n}} , such that the transition maps are holomorphic. The term "complex manifold" is variously...

label, such as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of...

each point in a domain in complex coordinate space ⁠ C n {\displaystyle \mathbb {C} ^{n}} ⁠. The existence of a complex derivative in a neighbourhood is...

the affine coordinate ring. A one-dimensional complex affine space, or complex affine line, is a torsor for a one-dimensional linear space over C {\displaystyle...

topological space. In particular, it is any non-empty connected open subset of the real coordinate space Rn or the complex coordinate space Cn. A connected...

singularities allowed Complex coordinate space, the set of all ordered n-tuples of complex numbers Complex Hilbert space, a complex inner product space that is also...

functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space C n {\displaystyle \mathbb...

case we obtain real coordinate space Rn. The field of complex numbers gives complex coordinate space Cn. The a + bi form of a complex number shows that...

Hopf fibration. The unit sphere in complex coordinate space Cn+1 fibers naturally over the complex projective space CPn with circles as fibers, and there...

origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three...

coordinate system is called a Cartesian plane. The set R 2 {\displaystyle \mathbb {R} ^{2}} of the ordered pairs of real numbers (the real coordinate...

In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called...

physics, when we complexify a real coordinate space R n {\displaystyle \mathbb {R} ^{n}} we create a complex coordinate space C n {\displaystyle \mathbb {C}...

In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real...

topological space. In particular, in real and complex analysis, a domain is a non-empty connected open subset of the real coordinate space R n {\displaystyle...

a qubit can be described as a single point in a 2-dimensional complex coordinate space. Furthermore, a set of n bits can be represented by n binary digits...

convenient, the Clifford torus can be viewed as residing inside the complex coordinate space C2, since C2 is topologically equivalent to R4. The Clifford torus...

hyperbolic complex space is a Hermitian manifold which is the equivalent of the real hyperbolic space in the context of complex manifolds. The complex hyperbolic...

product, but is ad hoc. The complexification of real coordinate space Rn is the complex coordinate space Cn. Likewise, if V consists of the m×n matrices with...

A one-dimensional space (1D space) is a mathematical space in which location can be specified with a single coordinate. An example is the number line,...

frames of reference. A basis B of a vector space V over a field F (such as the real numbers R or the complex numbers C) is a linearly independent subset...

real coordinate space, so is sometimes denoted R1 when comparing it to higher-dimensional spaces. The real line is a one-dimensional Euclidean space using...

article "Number/Complex Numbers". Analytic continuation Circular motion using complex numbers Complex-base system Complex coordinate space Complex geometry Geometry...

within it. 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...

defined on a real coordinate space where the distance between two points is the greatest of their differences along any coordinate dimension. It is named...