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(PDF) A Study on the Linear Algebra & Matrix in Mathematics

Source: researchgate.net

1. Linear algebra is a branch of mathematics that studies vectors, vector spaces, linear maps, and systems of linear equations.

2. Vector spaces are widely used in modern mathematics and have applications in abstract algebra, functional analysis, analytic geometry, and operator theory.

3. Linear algebra is important in solving linear problems in various fields such as the natural sciences and social sciences, as nonlinear models can often be approximated by linear ones.

The article titled "A Study on the Linear Algebra & Matrix in Mathematics" provides an overview of linear algebra and its applications. However, there are several issues with the article that need to be addressed.

Firstly, the article lacks proper citations and references. It mentions various concepts and terms without providing any sources to support these claims. This raises questions about the credibility and accuracy of the information presented.

Additionally, the article seems to rely heavily on Wikipedia as a source of information. Multiple sections of the article include direct links to Wikipedia pages as references. While Wikipedia can be a useful starting point for research, it is not considered a reliable academic source due to its open-editing nature.

Furthermore, the article does not provide a balanced view of linear algebra. It focuses primarily on its applications in abstract algebra and functional analysis but fails to mention other important areas such as numerical linear algebra or computational linear algebra. This narrow focus limits the scope of the study and may lead readers to believe that linear algebra is only relevant in certain fields.

Moreover, there is a lack of critical analysis in the article. It does not explore potential limitations or drawbacks of using linear algebra in various applications. For example, while it mentions that nonlinear models can often be approximated by linear ones, it does not discuss the potential inaccuracies or limitations of such approximations.

The article also contains promotional content for specific universities and departments. The authors mention their affiliations and email addresses, which gives the impression that they are promoting their own work rather than providing an objective study on linear algebra.

Overall, this article lacks proper citations, presents a one-sided view of linear algebra, relies heavily on unreliable sources like Wikipedia, and contains promotional content. It would benefit from more thorough research, balanced reporting, and critical analysis of the topic at hand.

Numerical linear algebra applications and techniques
Computational linear algebra algorithms and methods
Limitations of linear algebra in nonlinear modeling
Critiques of linear algebra in various fields
Alternative approaches to linear algebra in mathematics
Comprehensive overview of linear algebra applications and theories