for a given matrix

USAGE SUMMARY

The phrase "for a given matrix" is correct and usable in written English.
It can be used in mathematical or computational contexts when discussing properties, operations, or characteristics related to a specific matrix. Example: "The determinant can be calculated for a given matrix using various methods, including row reduction."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

29 human-written examples

For a given matrix (27).

Advances in Difference Equations

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

Journal of Inequalities and Applications

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

Journal of Inequalities and Applications

The essential uniqueness condition for a given matrix factor in PARALIND models makes use of Kruskal's permutation lemma[52, 86].

EURASIP Journal on Advances in Signal Processing

For a given matrix A, we use |A|:=sup_{xneq0}frac{|Ax|}{|x|} to denote its norm.

Journal of Inequalities and Applications

For a given matrix A ∈ M 2 , it is known (see [2, 3]) that the corresponding linear system.

Boundary Value Problems

Human-verified similar examples from authoritative sources

Similar Expressions

31 human-written examples

The next result deals with a necessary and sufficient condition for the extendability of a given matrix function on the hypersurface to an -monogenic function in or in, vanishing at infinity.

Boundary Value Problems

Due to diversity of modern computer architectures, each of the algorithms described here may be the method of choice for a particular hardware and a given matrix size.

Applied Mathematics and Computation

A large number of different null matrix configurations are possible for a given input matrix and we may wish to avoid undersampling ; however, at the same time very large ensembles can make the calculation of significance computationally intractable.

F1000Research

In this paper, we present an extended software OptQC, which finds permutation matrices P and Q for a given unitary matrix U such that the number of gates in the quantum circuit of U= QTPTU′PQ is significantly reduced, where U′ is equivalent to U up to a permutation and the quantum circuit implementation of each matrix component is considered separately.

Computer Physics Communications

For a given Toeplitz matrix, here R, we can construct an asymptotically equivalent circulant M × M matrix C in the sense that [36] (47).

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When using "for a given matrix", ensure the context clearly defines how the matrix is "given" (e.g., provided as input, defined by previous steps).

Common error

Avoid using "for a given matrix" without specifying where the matrix comes from or how it's defined. The term 'given' implies prior definition or provision, so ensure this is clear to the reader.

Linguistic Context

The phrase "for a given matrix" functions as an adjectival phrase modifying an implied clause. It sets a condition or context for a mathematical or computational statement, indicating that a specific matrix is the starting point. Ludwig AI confirms the phrase is correct and usable.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

The phrase "for a given matrix" is a common and grammatically correct phrase used primarily in scientific and technical contexts. It serves to specify that a particular matrix is the starting point or condition for further discussion or analysis. As Ludwig AI confirms, the phrase is well-established in academic and scientific literature. When using this phrase, ensure the context clearly defines how the matrix is "given" to avoid ambiguity. Consider using alternatives like "with a specified matrix" or "for a specific matrix" depending on the nuance you want to convey.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

given a specific matrix

Emphasizes the presence of a defined matrix, swapping the order of adjectives.

with a specified matrix

Replaces "given" with "specified", emphasizing the act of defining the matrix.

for a particular matrix

Substitutes "given" with "particular", highlighting a specific instance.

for a designated matrix

Replaces "given" with "designated", indicating a pre-selected matrix.

considering a certain matrix

Uses "considering" to introduce the matrix as a subject of analysis.

regarding a defined matrix

Uses "regarding" to introduce the matrix as a focus of attention.

in the context of a matrix

Focuses on the matrix as the context for further operations or analyses.

with a predetermined matrix

Highlights that the matrix has been decided in advance.

assuming a known matrix

Emphasizes that the matrix is already established or known.

when a matrix is provided

Highlights the provision of a matrix as a condition.

FAQs

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

Use "for a given matrix" to introduce a scenario or condition where a particular matrix is the starting point for further analysis or operations. For example, "The determinant can be calculated "for a given matrix" using row reduction."

What does "given" mean in the context of "for a given matrix"?

In this context, "given" implies that the matrix is already defined, provided, or assumed to be known before proceeding with any further steps or calculations. It's like saying "assuming we already have this matrix."

Is it better to say "for a given matrix" or "for a specific matrix"?

Both phrases are acceptable, but ""for a given matrix"" implies that the matrix is already known or provided, whereas "for a specific matrix" simply refers to a particular matrix without necessarily implying pre-existence.

What is the difference between "for a given matrix" and "for any matrix"?

"For a given matrix" refers to a particular, already-defined matrix. "For any matrix" refers to a statement or operation that applies to all matrices meeting certain criteria.