Linear Algebra is used in solving Science and Engineering problems, which in many cases can be formulated as linear system of equations, or eigenvalue problems and its generalized version and hence, amenable to solution using linear algebraic methods.

Also many nonlinear problems can be approximation by a linear representation over a region of problem variables space, linear algebraic methods can be used to obtain approximate solutions in this situation to the nonlinear problem.

In general linear algebra finds applications over a vast domain of modern science and engineering studies, it is used in data analysis, signal processing , operations research and optimization studies, dynamical systems analysis and control and also in studies of Computational Chemistry problems, Quantum mechanics and Quantum information theory.

Here’s just a fraction of what you can do with linear algebra:

https://medium.com/@jeremyjkun/here-s-just-a-fraction-of-what-you-can-do-with-linear-algebra-633383d4153f

The following link is useful

http://vmls-book.stanford.edu/vmls.pdf

واحدة من أهم تطبيقات الجبر الخطي والالكترونيات هو تحليل الدوائر الإلكترونية التي لا يمكن وصفها باستخدام قواعد المقاومات في سلسلة أو موازية مثل واحد هو مبين للحق. والهدف من ذلك هو لحساب التيار المار في كل فرع من فروع الدائرة أو لحساب الجهد في كل عقدة من الدائرة.

للجبر الخطي تطبيقات كثيره واحب التطبيقات لي هو استخدامه في حل المعادلات الخطيه وفي تشفير المعلومات

للجبر الخطي تطبيقات كثيره واحب التطبيقات لي هو استخدامه في حل

المعادلات الخطيه وفي التشفير ا

There is

للجبر الخطي تطبيقات كثيره واحب التطبيقات لي هو استخدامه في حل المعادلات الخطيه وفي تشفير

Linear Algebra is a continuous form of mathematics and is applied throughout science and engineering because it allows you to model natural phenomena and to compute them efficiently. 

The neatest application of linear algebra is Google’s PageRank algorithm which makes Google such a strong search engine.

you can see this link :

https://mathstats.uncg.edu/sites/yasaki/publications/machado-google-pagerank-linear-algebra-project.pdf

I agree with Dr Ali

For structural static and dynamic response, for analysis of elstic and plastic structural elements, soil dynamic response etc

There are many applications of linear algebra in electrical circuits, organic chemistry, and cryptography

specially since the science of cryptography its beginning was based on the basics of linear algebra

Che, S., Beckmann, B. M., & Reinhardt, S. K. (2017). Programming GPGPU graph applications with linear algebra building blocks. International Journal of Parallel Programming, 45(3), 657-679.

Linear algebra with applications..

Williams, G. (2017). Linear algebra with applications. Jones & Bartlett Learning.

Theory and applications...

Beilina, L., Karchevskii, E., & Karchevskii, M. (2017). Numerical linear algebra: Theory and applications. Springer International Publishing.

Its most practical applications are in Computer sciences (e.g., Artificial Intelligence) Engineering sciences, Economics, Medical Sciences, Space Science, Earth Sciences, Physics, Chemistry Biology, Bioinformatics,...almost every Science and logic.

Many mathematical fields depends on linear algebra (e.g. Operations research, Graph theory ,Modules,...etc ).

Many mathematical fields depend on linear algebra( Graph theory, Operations research, Modules,...etc). I think the book ( linear algebra) by Kolmann is very good reference.

Linear algebra has many applications that almost enter all sciences, and for more information you can review Introduction to linear algebra with application by Kulmann

Linear Algebra applications in most applied sciences. We use linear algebra in teaching group theory courses and applications in the field of spectroscopy. This field is important for understanding the partial structure of chemical compounds.

Used in reliability estimation, can be used in AI, for dynamic and structural response and analysis.

I think that most of scientific fields, espicially Engineering have applications of linear algebra.

For your reference

one of the most important applications is the representation theory, you can deql with symmetric groups as matrices . This idea leads to a revolution in Quantum mechanics.

Another application is Computer Science.Matrices plays an important role in these studies

Nice work

Linear Algebra is very useful in the study of anything in the space due to the particles moving in the space in different directions

Please take a look at the attached file and please note that as it has been mentioned above, there are many applications of Linear Algebra. The following list highlights a few of them.

In my opinion, Linear Algebra has 80 % of all Mathematic applications. In last time it is the techniques of AI and ML as well.

1 - The application for image processing and compressing:

Each image is made up of a relatively large number of small squares called pixels (image elements), and linear algebra techniques are used to increase image compression or rebuild. The second use is in image processing such as optimization, restoration, and segmentation. Each image can be represented as a matrix n by n and is applicable to matrix operations in linear algebra

2 - Application to Encryption:

Encryption as we know is the conversion of data into an unreadable data form. The coding matrix, the master matrix, and the decoding matrix are all possible to perform matrix operations in linear algebra.

3 - Application to find eigenvalues ​​(roots) of stability in contrl systems

We use linear algebra In many applications ,electrical circuit ,genetic and cryptography. Polygraphic System

Another way of encoding is to divide plain text into sets of n-letters, and replace them with n code letters. In this case invertible matrices can be used to provide a better coding, than substitution.