i-th component

USAGE SUMMARY

"i-th component" is a correct and usable phrase in written English.
It is typically used in mathematical or technical writing to refer to a specific component in a series or list, where "i" represents a variable or numerical value. Example sentence: The equation for calculating the velocity of a falling object includes the acceleration due to gravity as its i-th component.

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

22 human-written examples

Overall molar fraction of i-th component.

Journal of Petroleum Exploration and Production Technology

w1, i and w2, i are the i-th component of vectors w1 and w2, respectively.

EURASIP Journal on Wireless Communications and Networking

x i 1 and x i 2 are first parent and second parent's i-th component.

Journal of Industrial Engineering International

Subscript (alpha=M_{i}) or E refers to the mass balance equation of the i-th component or to the energy balance equation, respectively.

Journal of Mathematics in Industry

Where S i is the i-th singular value of Φ, α i and y ˜ i are the i-th component of α and y ˜ = U T y, respectively.

EURASIP Journal on Wireless Communications and Networking

Denote by ( {overline{mathbf{t}}}_{I-i}=left[{overline{t}}_j:jin I,jne iright] ) the vector ( {overline{mathbf{t}}}_I ) deprived from its i-th component, ( {overline{t}}_i ).

European Transport Research Review

Human-verified similar examples from authoritative sources

Similar Expressions

38 human-written examples

where i denotes the i th component of vector.

Journal of Inequalities and Applications

where is the i th component of vector.

EURASIP Journal on Advances in Signal Processing

As the i th component code has length n i, the cyclic code must be shortened.

EURASIP Journal on Wireless Communications and Networking

All vectors x are column vectors where x i is the i th component.

EURASIP Journal on Advances in Signal Processing

where x i (i = 1, 2, …, K) is the i th component of X.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When using "i-th component" in technical writing, clearly define 'i' to avoid ambiguity. For example, state that 'i' represents an index or a specific element within a set.

Common error

Avoid using "i-th component" without properly defining the range or context of 'i'. This can lead to confusion if the reader doesn't understand what 'i' represents in your specific application.

Linguistic Context

The phrase "i-th component" functions as a modifier and identifier, specifying a particular element within a sequence or structure. Ludwig AI confirms that it typically appears in technical and scientific contexts to pinpoint a specific part, as demonstrated in the examples.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, the phrase "i-th component" is a common and grammatically sound technical term used to precisely identify a specific element within a series, vector, or structure. Ludwig AI underscores its prevalent use in scientific and mathematical contexts. To ensure clarity, always define 'i' when using this phrase, as per the writing guidance. While alternatives like "ith element" may sometimes be suitable, "i-th component" specifically implies a part that contributes to a whole. The term's high frequency in scientific literature signifies its importance in technical communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

ith element

This alternative changes "component" to "element", which provides a more general term for a part of a whole.

ith member

This alternative uses "member" instead of "component", suggesting that it is part of a set or group.

ith item

This alternative utilizes "item" instead of "component", presenting the part as a discrete unit within a series.

ith entry

This option substitutes "component" with "entry", implying that it is one record in a data set.

ith constituent

Replacing "component" with "constituent" indicates a part that makes up a larger structure or entity.

ith factor

Switching from "component" to "factor" denotes that it's one of several elements contributing to a result.

ith aspect

Using "aspect" instead of "component" presents it as a particular feature or angle of something.

ith portion

Replacing "component" with "portion" refers to a specific quantity or part of something.

the ith part

Rephrasing the sentence to use the more common phrase "the ith part" provides an easier readability and general term.

component number i

This version reverses the phrase order to emphasize the component and clarifies which item number we are referring to.

FAQs

How do I use "i-th component" in a sentence?

Use "i-th component" to refer to a specific element within a series, vector, or set, where 'i' is a numerical index. For instance: "The algorithm modifies the value of the "i-th component" in the data array".

What can I say instead of "i-th component"?

You can use alternatives like "ith element", "ith member", or "ith entry" depending on the context.

What's the difference between "i-th component" and "ith element"?

While "i-th component" and "ith element" are often interchangeable, "component" may imply a part that contributes to a whole, whereas "element" is a more general term for an item in a set.

Is it necessary to define 'i' when using the term "i-th component"?

Yes, defining 'i' is crucial for clarity. Explain its role (e.g., index, counter) and its valid range to prevent misinterpretation. This is especially important in mathematical or technical documentation.