by applying the matrix

USAGE SUMMARY

The phrase "by applying the matrix" is correct and usable in written English.
You can use it when discussing the process of utilizing a matrix in a mathematical, analytical, or computational context. Example: "By applying the matrix, we can determine the optimal solution to the problem."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

7 human-written examples

Note that (28) is obtained from (27) by applying the matrix inversion lemma, and using the fact that.

EURASIP Journal on Advances in Signal Processing

By applying the matrix decomposition, we get ({hat {mathbf {Q}}}_{mathbf {v}}=hat {mathbf {v}}{hat {mathbf {v}}}^{H}).

EURASIP Journal on Wireless Communications and Networking

These three values are used as output values by applying the matrix related to the weights ((a_{i,j})) in Eq. (3).

ROBOMECH Journal

Specifically, by applying the matrix inversion lemma to the 2×2 block matrix B−1 with diagonal blocks, it can be shown that the trace in (54) is applied on a sum of diagonal matrices.

EURASIP Journal on Advances in Signal Processing

and finally by applying the matrix inversion lemma lambda_{{mathbf{K}}}=beta_{infty} left[2Lambda_{mathrm{u}}-mu m_{mathrm{f}}^{(2,2 }Lambda_{mathrm{u}}^{2}right]^{-1}lambda_{mathrm{u}}.

EURASIP Journal on Advances in Signal Processing

By applying the matrix inversion lemma to the MMSE solution of Equation (16) and considering afterwards the limiting case when ξ t → 0, the expressions for the ZF linear precoder can be readily obtained and expressed as follows F ZF = g ZF - 1 H H H H H H ) - 1, g ZF = tr H H H 1 1 C u E tx. (17).

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

53 human-written examples

Such a tedious task can be turned into a breeze by repeatedly applying the matrix identities [29] ( I + U ) − 1 = I − U ( I + U ) − 1, V ( I + U V ) − 1 = ( I + V U ) − 1 V. (14).

Journal of Inequalities and Applications

Moreover, the time-dependent stability conditions are derived by applying the linear matrix inequality (LMI).

Journal of the Franklin Institute

The first example shows the identification of the significant patterns of fracture intensity categories by applying the probability matrix.

International Journal of Rock Mechanics and Mining Sciences

The analytic expressions of the transmission amplitude and conductance are derived by applying the transfer matrix method in the one-electron scattering formalism.

Physics Letters A

The linear and non-linear (large amplitude), axisymmetric free vibration of a circular plate of variable thickness, with immovable edges, is analyzed by applying the transfer matrix method.

Journal of Sound and Vibration

Expert writing Tips

Best practice

When describing mathematical or computational processes, ensure that the specific matrix being applied is clearly defined and its purpose is well explained.

Common error

Avoid simply stating that something is done "by applying the matrix" without specifying what kind of matrix is being applied and the specific operation involved. Provide enough context for the reader to understand the process.

Linguistic Context

The phrase "by applying the matrix" functions as a prepositional phrase that introduces a method or technique. Ludwig's examples confirm this usage, demonstrating its role in describing how a matrix is used to achieve a specific outcome. The phrase specifies the means by which an action is performed.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

The phrase "by applying the matrix" is a grammatically correct prepositional phrase commonly used in scientific and technical contexts. It describes a method or technique where a matrix is used to achieve a specific outcome. According to Ludwig, the phrase is most frequently found in scientific publications, indicating its formal and technical register. While the phrase is generally acceptable, it's crucial to provide sufficient context about the specific matrix and its application to avoid vagueness. Alternatives such as "through matrix application" or "using matrix implementation" can be used for variety. By understanding its grammatical function, communicative purpose, and appropriate register, writers can effectively utilize "by applying the matrix" in their writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

through matrix application

Emphasizes the act of applying the matrix as a method or process.

using matrix implementation

Focuses on the practical implementation of a matrix in a system or model.

via matrix transformation

Highlights the transformation aspect achieved through the matrix.

with matrix utilization

Stresses the use or consumption of the matrix for a specific purpose.

leveraging matrix operations

Suggests taking advantage of the capabilities provided by matrix operations.

employing matrix algebra

Specifically refers to the use of matrix algebra principles.

by means of a matrix

A more formal way of stating that a matrix is the tool being used.

through the matrix method

Highlights the use of a matrix as a structured method or technique.

by way of matrix manipulation

Focuses on the manipulation or alteration of a matrix to achieve a result.

utilizing a matrix-based approach

Describes the overall strategy as being based on matrices.

FAQs

How can I use "by applying the matrix" in a sentence?

You can use "by applying the matrix" to describe a process where a matrix is used to transform or analyze data. For example, "The data was normalized "by applying the matrix" transformation to each data point."

What are some alternatives to "by applying the matrix"?

Some alternatives include "through matrix application", "using matrix implementation", or "via matrix transformation", depending on the specific context.

Is it correct to say "by applying the matrix" in scientific writing?

Yes, "by applying the matrix" is grammatically correct and commonly used in scientific writing to describe mathematical or computational processes.

What does it mean to solve a problem "by applying the matrix"?

Solving a problem "by applying the matrix" means using matrix operations, such as multiplication, inversion, or decomposition, to find a solution or transform the problem into a more manageable form.