a given matrix

USAGE SUMMARY

The phrase "a given matrix" is correct and usable in written English.
It can be used in mathematical or computational contexts when referring to a specific matrix that has been defined or is being discussed. Example: "To solve the equation, we need to analyze the properties of a given matrix."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The flashtube situated behind a given matrix emits its beam of light each time that the component of the lens finds itself, in the course of its to-and-fro movement, in the axis that joins this matrix to the position where the letter to which it corresponds is to appear in the line to be composed on the sensitive film.

Encyclopedia Britannica

For a given matrix (27).

Advances in Difference Equations

For a given matrix, its spectral decomposition is (2.1).

Journal of Inequalities and Applications

The matrix is a given matrix such that.

EURASIP Journal on Advances in Signal Processing

where the operator # returns the pseudo-inverse of a given matrix.

EURASIP Journal on Wireless Communications and Networking

However, the (l_{p} -null space property is difficul_{p} -nullecked for a given matrix.

Journal of Inequalities and Applications

where is a given matrix of while and are unknown parameters.

Journal of Inequalities and Applications

The low-rank approximation of a given matrix is a frequent problem in data analysis [40].

EURASIP Journal on Advances in Signal Processing

Recovering the low-rank, sparse components of a given matrix is a challenging problem that arises in many real applications.

Neural Networks

Our results imply that there is a logspace algorithm that decides whether a given matrix has this property.

Journal of Discrete Algorithms

The problem of finding the least change adjustment to a given matrix pencil is considered in this paper.

Applied Mathematics and Computation

Expert writing Tips

Best practice

When using "a given matrix", ensure the context clearly establishes which matrix you are referring to. This avoids ambiguity, especially in mathematical or computational discussions.

Common error

Avoid using "a given matrix" without clearly defining or referencing it previously. Always introduce the matrix before using the phrase to ensure readers understand which matrix is being discussed.

Linguistic Context

The phrase "a given matrix" functions as an adjectival phrase modifying the noun "matrix". It specifies that the matrix being referred to is already known or defined within the context of the discussion. Ludwig AI confirms this usage through numerous examples in scientific and technical literature.

Expression frequency: Very common

Frequent in

Science

96%

Encyclopedias

2%

News & Media

0%

Less common in

Formal & Business

0%

Academia

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "a given matrix" is a common term, especially in technical and academic contexts. As Ludwig AI confirms, it indicates a matrix that is already defined or understood within the current discussion. It functions adjectivally to specify a particular matrix and is most frequently encountered in scientific literature. Alternative phrasings include "a specified matrix" or "a particular matrix", offering subtle differences in emphasis. When using "a given matrix", clarity and context are key to ensuring effective communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a specified matrix

Replaces "given" with "specified", indicating a matrix that has been explicitly designated.

a defined matrix

Substitutes "given" with "defined", suggesting the matrix has been previously established with clear parameters.

a particular matrix

Uses "particular" instead of "given", highlighting that the matrix is a specific instance under consideration.

a known matrix

Replaces "given" with "known", implying that the properties of the matrix are already understood.

a designated matrix

Emphasizes that the matrix has been officially assigned or indicated for a specific purpose.

a pre-determined matrix

Indicates the matrix was established or decided in advance.

a set matrix

Implies that the matrix is fixed or established.

an established matrix

Replaces "given" with "established", meaning that the matrix is already recognized or accepted.

a fixed matrix

Highlights that the matrix is unchangeable or constant.

a provided matrix

Suggests the matrix has been supplied or made available for use.

FAQs

How can I use "a given matrix" in a sentence?

You can use "a given matrix" when you want to refer to a matrix that has already been defined or is understood within a specific context. For example, "Analyze the eigenvalues of "a given matrix" to determine its stability".

What's an alternative to saying "a given matrix"?

Alternatives include "a specified matrix", "a defined matrix", or "a particular matrix". The choice depends on the specific nuance you want to convey.

When is it appropriate to use "a given matrix"?

It's appropriate when discussing mathematical or computational problems where the matrix being analyzed is already established or understood. This avoids unnecessary repetition or redefinition.

Is "a given matrix" formal or informal?

The phrase "a given matrix" is generally considered formal and is suitable for academic, scientific, and technical writing. It's not typically used in informal conversation.