element wise

USAGE SUMMARY

The phrase "element wise" is correct and usable in written English.
It is used to refer to individual components of a larger entity, usually when a comparison is being made between them. For example, "The students of our class showed improvement element wise, with each student succeeding in different areas."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

5 human-written examples

T and.∗ denote the transpose and the element wise conjugation, respectively.

EURASIP Journal on Wireless Communications and Networking

The superscripts T,∗, ‡ represent the transpose, transpose conjugate, and element wise conjugate.

EURASIP Journal on Wireless Communications and Networking

For the case of binary PSK (BPSK) the projection involves the element wise multiplication of the two vectors while for QPSK the real and imaginary parts of the elements need to be separated prior to element wise multiplication (16).

EURASIP Journal on Wireless Communications and Networking

This can be expressed by the element wise multiplication of the data symbols with a scrambling sequence (12).

EURASIP Journal on Wireless Communications and Networking

where the modulus operator is assumed to be applied element wise and the function returns the mean of a vector.

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

55 human-written examples

The optimization procedure renders element-wise values of these parameters.

Computer-Aided Design

If the first arg is a Vector the reduce is done element-wise.

Yale University

The specified subsequences of sequence-1 and sequence-2 are compared element-wise.

Massachusetts Institute of Technology

We define a new "element-wise" product, which greatly simplifies the likelihood function with hyperparameter matrix.

Astronomy and Computing

We added the input and the output from the third Conv block in an element-wise manner.

Nature

The functional form and corresponding parameters are determined element-wise by solving a combinatorial optimization problem.

Chemical Engineering Science

Expert writing Tips

Best practice

When describing mathematical or computational operations on arrays or matrices, use "element wise" to clearly indicate that the operation is applied to each element independently. For instance, "perform an element wise multiplication of the two vectors".

Common error

Avoid using "element wise" when you are referring to operations that apply to the entire array or matrix as a single unit, rather than individual elements. For instance, use "matrix multiplication" instead of "element wise multiplication" if you are performing standard matrix multiplication.

Linguistic Context

The phrase "element wise" functions as an adjective, modifying nouns like "multiplication", "operation", or "comparison". It specifies that the action or attribute applies to individual elements rather than the whole structure. Ludwig AI confirms that it's grammatically correct.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

The phrase "element wise" is a grammatically correct adjective phrase primarily used in scientific and technical writing to specify that an operation or comparison applies to individual elements within a data structure (such as a matrix or vector). While not frequently encountered, its use ensures clarity. Ludwig AI analysis validates its correctness, but suggests it's more technical. When writing, remember to use "element wise" to denote operations on individual components, and consider alternatives like "component-wise" for broader audience. Common errors include misapplying it to entire array operations.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

component-wise

Replaces "element" with "component", emphasizing the individual parts that make up a whole.

pointwise

Commonly used in mathematical contexts to describe operations performed on corresponding points or elements.

per element

Directly specifies that an action or property applies to each element.

term by term

Highlights a sequential process, focusing on each term or element in order.

for each element

Similar to "per element", but more explicitly states the scope of application.

by individual element

Adds emphasis to the distinct handling of each element.

individually

Emphasizes the separate and distinct consideration of each element.

with respect to each element

More formal and precise, suitable for technical or mathematical writing.

at each position

Focuses on the location or index of the element within a structure.

Hadamard-wise

Specifically refers to operations following the Hadamard product, applicable to matrices.

FAQs

How can I use "element wise" in a sentence?

"Element wise" is used to describe operations that are applied to each individual element of a vector or matrix. For example, "The calculation involves an "element wise multiplication" of two matrices."

What is an alternative to saying "element wise"?

Depending on the context, you could use phrases like "component-wise", "pointwise", or "term by term" as alternatives to "element wise". These options highlight the individual treatment of each part of a structure.

Is "element-wise" hyphenated or not?

Both "element wise" (two words) and "element-wise" (hyphenated) are acceptable, though the hyphenated form is more common in technical writing. The meaning remains the same.

What's the difference between "element wise" and operations on the entire matrix?

"Element wise" operations apply to each individual element, whereas operations on the entire matrix consider the matrix as a single entity. For instance, inverting a matrix is not an "element wise operation", but scaling each element by a constant is.