Hello,

Matrix is one of the main and non-avoidable topic of linear algebra. For learning the importance and uses of matrix, you must know the importance of linear algebra

Having studied Engineering, I can tell you that Linear Algebra is fundamental and an extremely powerful tool inevery singlediscipline of Engineering.



If you are reading this and considering learning linear algebra then I will first issue you with a warning: Linear algebra is mighty stuff. You should be both manically excited and scared by the awesome power it will give you!!!!!!



In the abstract, it allows you to manipulate and understand whole systems of equations with huge numbers of dimensions/variables on paper without any fuss, and solve them computationally. Here are some of the real-world relationships that are governed by linear equations and some of its applications:



Load and displacements in structures



Compatability in structures



Finite element analysis (has Mechanical, Electrical, and Thermodynamic applications)



Stress and strain in more than 1-D



Mechanical vibrations



Current and voltage in LCR circuits



Small signals in nonlinear circuits = amplifiers



Flow in a network of pipes



Control theory (governs how state space systems evolve over time, discrete and continuous)



Control theory (Optimal controller can be found using simple linear algebra)



Control theory (Model Predictive control is heavily reliant on linear algebra)



Computer vision (Used to calibrate camera, stitch together stereo images)



Machine learning (Support Vector Machine)



Machine learning (Principal component analysis)



Lots of optimization techniques rely on linear algebra as soon as the dimensionality starts to increase.



Fit an arbitrary polynomial to some data.



Arbitrarily large problems of the types listed above can be converted into simple matrix equations, and most of those equations are of the formA x = b. Nearly all other problems are of the formA x =  x. Yep, you read that right! Nearly all engineering problems, no matter how huge, can be reduced to one of two equations!



Linear algebra is so powerful that it also deals with small deviations in lots of non-linear systems! A typical engineering way to deal with a non-linear system might be to linearize it, then use Linear Algebra to understand it!



Hope it helps

Hey Akash! Every time it is not possible that there is a direct link between topic and the application of that topic in the branch, there may be indirect link of the topic which may helps you in future to understand some other things. They are used for identifying the stability of a system, for performing transformations on system equations, Signal processing and communication etc. And in almost every application they stand the purpose of being a mathematical tool to make our lives easier.