complex dimension

USAGE SUMMARY

The phrase "complex dimension" is correct and usable in written English.
It can be used in mathematical or scientific contexts, particularly in discussions about geometry, algebra, or theoretical physics. Example: "In the study of complex analysis, we often explore the properties of functions defined in a complex dimension."

✓ Grammatically correct

Science

Academia

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

In addition to this exploitation, this receiver reduces the system detection complexity by one complex dimension and is thus also applicable to single antenna UEs, which do not possess spatial degrees of freedom to cancel or attenuate the interference via ZF or MMSE filters.

EURASIP Journal on Wireless Communications and Networking

Its low complexity is based on the reduction of one complex dimension.

EURASIP Journal on Wireless Communications and Networking

Our proposed low-complexity interference-aware receiver structure not only reduces one complex dimension of the system but is also characterized by exploiting the interference structure in the detection process.

EURASIP Journal on Wireless Communications and Networking

So if x2 belongs to QAM256, then instead of searching 256 constellation points for the minimization of (14), the metric (15) reduces it to merely two operations thereby trimming down one complex dimension in the detection, i.e., the detection complexity is independent of |χ2| and reduces to.

EURASIP Journal on Wireless Communications and Networking

Here, we propose a low-complexity interference-aware receiver structure that on one hand reduces one complex dimension of the system while on the other hand, it exploits the interference structure in the detection process.

EURASIP Journal on Wireless Communications and Networking

For example, curves have (complex) dimension one and surfaces have (complex) dimension two.

Encyclopedia Britannica

Letsdenote the complex dimension ofK/T.

Journal of Functional Analysis

Let X be a compact Kähler manifold of complex dimension m.

Journal of Functional Analysis

For another example, the case of complex dimension two, i.e. of algebraic surfaces, has unexpected links to the study of four dimensional topology.

Columbia University

Since the complex numbers involve two real parameters, a surface, which is two-dimensional over the real numbers, has only one complex dimension and is sometimes called a complex curve.

The Guardian

Human-verified similar examples from authoritative sources

Similar Expressions

1 human-written examples

Applications will consolidate many kinds of measurements in a single dashboard and allow us to analyze ourselves across ever more complex dimensions.

Harvard Business Review

Expert writing Tips

Best practice

When discussing mathematical or scientific concepts, ensure that the context clearly indicates whether you are referring to real or "complex dimensions". This avoids ambiguity and enhances understanding.

Common error

Avoid using "complex dimension" interchangeably with real dimensions without specifying the mathematical context. Complex dimensions involve complex numbers, each having a real and imaginary part, which affects calculations and interpretations.

Linguistic Context

The phrase "complex dimension" functions as a technical noun phrase, primarily used in mathematics and sciences. It specifies the dimensionality of a space or object defined using complex numbers. Ludwig examples confirm its use in describing system complexity and mathematical manifolds.

Expression frequency: Very common

Frequent in

Science

78%

Academia

14%

News & Media

3%

Less common in

Encyclopedias

3%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

The term "complex dimension" is a precise and technical noun phrase widely employed in scientific and academic contexts, particularly in mathematics and physics. As Ludwig AI confirms, it accurately describes the dimensionality of spaces or objects defined using complex numbers. Its primary function is to quantify the size or extent of a mathematical construct. While its use is prevalent in formal and scientific registers, it's less common in general or informal settings. Understanding its proper context, distinguishing it from real dimensions, and avoiding ambiguity are essential for correct usage.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

complex space

Refers to the mathematical space defined by complex numbers, similar to "complex dimension" in a geometric context.

complex manifold

Describes a manifold with complex coordinates, analogous to specifying a "complex dimension" in differential geometry.

number of complex parameters

Focuses on counting parameters in a complex system, similar to defining its "complex dimension".

complex degree of freedom

Highlights the independent parameters needed to describe a complex system, similar to "complex dimension".

dimensionality in the complex plane

Specifies the dimension within the complex number system, relating to "complex dimension".

complex variable count

Quantifies the number of complex variables, akin to describing the "complex dimension" of a space.

complex geometric extent

Describes the extent of a geometric object in the complex domain, related to "complex dimension".

complex algebraic size

Relates to the size of an algebraic object in a complex space, similar to "complex dimension".

order in complex analysis

Refers to the order of functions or spaces in complex analysis, loosely related to "complex dimension".

complex structural rank

Describes the rank of a complex structure, which can relate to the "complex dimension" of the system.

FAQs

How is "complex dimension" used in mathematics?

In mathematics, "complex dimension" refers to the number of complex coordinates needed to specify a point in a complex space or manifold. It is used extensively in complex analysis, algebraic geometry, and theoretical physics.

What's the difference between real and "complex dimension"?

Real dimensions use real numbers to define coordinates, while "complex dimensions" use complex numbers. Each complex number consists of a real and an imaginary part, effectively doubling the number of real dimensions needed to represent the same space. For example, a complex dimension of 1 corresponds to two real dimensions.

Where can I find examples of "complex dimension" in scientific literature?

You can find examples of "complex dimension" in journals related to mathematics, physics, and engineering, particularly in articles discussing complex analysis, algebraic geometry, signal processing, and quantum mechanics. Search engines like Google Scholar or databases like ScienceDirect are good starting points.

What are some alternative terms for "complex dimension" in certain contexts?

Depending on the context, you might use alternative terms such as "complex space", "complex manifold", or number of complex parameters. The most suitable term depends on the specific field and the concept you want to convey.