component-wise

USAGE SUMMARY

The phrase "component-wise" is correct and usable in written English.
It is typically used in mathematical or technical contexts to describe operations or comparisons that are performed on each corresponding element of two or more components, such as vectors or matrices. Example: "The two vectors can be added component-wise to produce a new vector."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

where ∘ denotes component-wise multiplication.

EURASIP Journal on Wireless Communications and Networking

Note that all computations are component-wise.

Journal of Inequalities and Applications

(2.2) the derivation ′ being understood component-wise.

Boundary Value Problems

where symbol denotes component-wise inequality.

EURASIP Journal on Wireless Communications and Networking

Operators, and denote factorial component-wise vector multiplication and component-wise vector division, respectively.

EURASIP Journal on Advances in Signal Processing

Here and hereafter, and are defined component-wise.

EURASIP Journal on Wireless Communications and Networking

where the inequality sign for vectors applies component-wise.

EURASIP Journal on Audio, Speech, and Music Processing

Similarly, the homomorphic subtraction is computed by component-wise subtraction.

Pacific Journal of Mathematics for Industry

Both the ⊗ and the division signs are component-wise operations.

EURASIP Journal on Advances in Signal Processing

The operator " ⊙" denotes the component-wise vector multiplication (Hadamard product).

EURASIP Journal on Advances in Signal Processing

The component-wise form is described as follows.

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using "component-wise", ensure it's clear what the 'components' are (e.g., elements of a vector, parts of a system). Be precise in your context to avoid ambiguity.

Common error

Avoid using "component-wise" when the operation affects the components in relation to each other. "Component-wise" implies each component is treated independently.

Linguistic Context

The phrase "component-wise" functions primarily as an adverbial modifier. It describes how an operation is performed, specifying that it is applied to individual components or elements, rather than to the entire structure as a whole. As Ludwig AI confirms, this phrase is correct and usable in written English.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, "component-wise" is a grammatically sound adverbial phrase predominantly used in scientific and technical fields. As confirmed by Ludwig AI, it clarifies that an operation is applied individually to each component of a data structure, like a vector or matrix. Alternatives such as "element-wise" and "per-element" offer similar meanings. It's crucial to use "component-wise" when each component is indeed treated independently, ensuring precision in your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

element-wise

Refers to operations performed on individual elements of a data structure.

per-element

Highlights the individual processing of each element.

element by element

Emphasizes the sequential nature of processing elements.

entry-wise

Focuses on individual entries within a matrix or vector.

pointwise

Often used in the context of functions, indicating operations applied at each point.

term by term

Used when referring to elements in a series or sequence.

individually

Highlights that each component is treated separately.

separate processing

Focuses on the independent handling of each component.

in each dimension

Emphasizes operating on corresponding parts across dimensions.

for each coordinate

Specifies operating on a coordinate by coordinate basis.

FAQs

How is "component-wise" used in mathematical contexts?

In mathematics, "component-wise" refers to performing an operation on corresponding elements of vectors or matrices, such as "component-wise" addition or multiplication.

What's a good alternative to "component-wise"?

Depending on the context, you can use "element-wise", "per-element", or "entry-wise" as alternatives to "component-wise".

When is it appropriate to use "component-wise"?

Use "component-wise" when you want to emphasize that an operation is applied to each individual component of a vector, matrix, or other data structure independently.

Is "component-wise" the same as "element-wise"?

Yes, "component-wise" and "element-wise" are often used interchangeably, especially in the context of vectors and matrices, to describe operations performed on corresponding elements.