equal dimensional

USAGE SUMMARY

The phrase "equal dimensional" is correct and usable in written English.
It can be used in contexts related to mathematics, physics, or any field where dimensions are compared or discussed. Example: "In this study, we focus on equal dimensional spaces to analyze the properties of the geometric figures."

✓ Grammatically correct

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

This approach has some inherent assumptions including: (a) that the gel undergoes equal dimensional changes during the fixation, embedding, sectioning and labelling processes and (b) that LE in the gel is the same as in the cell compartment of interest.

Histochemistry and Cell Biology

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

Thus the Fock space can be split up as a direct sum of two equal-dimensional eigenspaces of P, called the positive and negative parity subspaces: F ( C d ) = [ ⨁ i even ( ∧ i C d ) ] ⊕ [ ⨁ i odd ( ∧ i C d ) ].

EPJ Quantum Technology

The effective way to solve this aspect is to shift the wire during cutting by an amount which is equal to dimensional deviation.

Journal of Industrial Engineering International

equal) n-dimensional jointly measurable random processes { ψ t ; t ∈ [ 0, T ] } which satisfy: Evidently, H F 2 ( 0, T ; R n ) is a Banach space endowed with the canonical norm ∥ ψ ∥ = { E ∫ 0 T | ψ s | 2 d s } 1 2. E ∫ 0 T | ψ t | 2 d t < + ∞, ψ t is F t measurable, for a.e.

Boundary Value Problems

equal) n-dimensional jointly measurable random processes { ψ t ; t ∈ [ 0, T ] } which satisfy: Evidently, H F 2 ( 0, T ; R n ) is a Banach space endowed with the canonical norm ∥ ψ ∥ = { E ∫ 0 T | ψ s | 2 d s } 1 2. (i) E ∫ 0 T | ψ t | 2 d t < + ∞,   (ii) ψ t is F t measurable, for a.e.

Boundary Value Problems

All essential features of the methodology are present in one-dimensional and two-dimensional cases, although the schemes to be analysed lend themselves with equal to higher-dimensional case.

Journal of Computational Physics

Note that since trace and determinant are equal for one-dimensional signals, both definitions are equivalent in this case and results presented in [12] are obviously still valid.

Plosone

As Henri Bergson states: "Though all of the photographs of a city taken from all points of view indefinitely complete one another, they will never equal in value that dimensional object: the city along whose streets one walks".

The Guardian

Calculation of maximum lift coefficient can be approximately equal to the two dimensional section data minus 5%% due to the negative lift needed at the tailplane to maintain moment equilibrium.

European Transport Research Review

Here R is the equilibrium bond length, g a geometric factor of order 1 related to the area supported by the bond, k is a dimensional constant equal to 23 nN.Å, b is the bond valence softness parameter and q is the effective charge on the ions forming the bond.

Chemical Reviews

It also seems to have made possible the development of a pictorial, two-dimensional language equal to but different from the sculptural tradition already in place.

The New York Times - Arts

Expert writing Tips

Best practice

When describing geometric shapes or mathematical spaces, use "equal dimensional" to clearly indicate that they have the same number of dimensions. This is especially useful in scientific and technical writing where precision is essential.

Common error

Avoid using "equal dimensional" when you simply mean equal in size or volume. "Equal dimensional" specifically refers to the number of dimensions, not the magnitude of those dimensions. For example, two boxes can have equal volume but different dimensions.

Linguistic Context

The phrase "equal dimensional" functions as a descriptive adjective phrase. Ludwig AI suggests that it is used to characterize objects or spaces having the same number of dimensions. It modifies a noun, providing information about its dimensional properties.

Expression frequency: Rare

Frequent in

Science

66%

News & Media

19%

Encyclopedias

5%

Less common in

Formal & Business

4%

Reference

1%

Wiki

1%

Ludwig's WRAP-UP

In summary, "equal dimensional" is a phrase used to describe entities that have the same number of dimensions, predominantly in scientific and technical contexts. Ludwig AI analysis identifies its function as a descriptive adjective phrase with a formal register. While grammatically correct, as confirmed by Ludwig, its usage is relatively rare. Alternatives include "same dimension" or "identical dimensions", depending on the desired emphasis. When employing this phrase, ensure the context requires specifying the number of dimensions rather than simply indicating equal size or volume. Pay specific attention to its formal usage and use it accordingly.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

same dimension

Changes the adjective "equal" to "same", maintaining the core meaning of identical dimensions.

identical dimensions

Replaces "equal" with "identical" for a stronger emphasis on dimensional equivalence.

equivalent dimensions

Uses "equivalent" to suggest a functional or effective equality in dimensions, even if not perfectly identical.

proportional dimensions

Implies that the dimensions are not necessarily the same, but maintain a consistent ratio.

commensurate dimensions

Suggests the dimensions are appropriately related or proportional to each other.

uniform dimensions

Focuses on the consistency and regularity of the dimensions.

matching dimensions

Highlights that the dimensions correspond or align with each other.

corresponding dimensions

Emphasizes the relationship or connection between the dimensions being compared.

balanced dimensions

Suggests the dimensions are in equilibrium or harmony with each other.

symmetrical dimensions

Highlights that dimensions are mirrored or evenly distributed.

FAQs

How is "equal dimensional" used in scientific contexts?

In scientific fields like physics and mathematics, "equal dimensional" is used to describe spaces or objects that have the same number of dimensions. For example, comparing two spaces to determine if they both exist in two dimensions or three dimensions.

What's a good alternative to "equal dimensional" in less formal writing?

While less precise, you could use phrases like "same size" or "similar scale" depending on the context, though these alternatives don't directly address the dimensionality. For a more precise but still accessible term, consider "same dimension".

When is it appropriate to use "equal dimensional" over "equivalent dimensions"?

"Equal dimensional" focuses specifically on the number of dimensions being identical. "Equivalent dimensions" might imply a functional similarity or effective equality, even if the dimensions aren't numerically identical. The choice depends on whether you need to emphasize the exact count of dimensions or a broader sense of dimensional equivalence.

Is "equal dimensional" always the best way to describe objects that are the same size?

No. "Equal dimensional" is specific to the number of dimensions. If objects have the same size or volume but potentially different shapes or dimensionality, use phrases like "equal in size" or "same volume" instead. If they have the "same dimension", then it's the right choice.