Matrix theory is not just based on math and statistics but is also considered as a base for all courses and fields. There are many uses of matrices theory for all disciplines math, finance, economics, statistics, and applied sciences. There are some other applications of linear algebra in practical fields and here we will learn applications in applied mathematics.
Matrix theory and its application in Applied Mathematics:
The constructions of math models for solving systems of equations is common applications of matrix theory of Applied maths. here we will discuss this in detail.
- Phoet al in 2018 studied the algorithm of Newton and gave the max link function. This method comes with many applications for statistics and models of regression of missing data.
- In 2019 different newton methods regression models were used for decision sciences and education employed for matrix theory.
- Optim, Nleqslv used matrix theory for defining parameters for regression models and best to use for R programmed by the Newton method.
- With that moment generating function expectation and changes in ubiquitous distribution for application in decision sciences. Pho et al reviewed the 4 solution techniques for decision sciences; bisection, gradient, secant, and Newton methods.
- While Song et al. give the Cramer rule for the unique root of restricted matrix equation with the quaternion skew fields, JI used explicit formulas of the generalized inverses and condensed Cramer rule.
- EEvibes is an online teaching website where you can get different courses based on electrical engineering. Also, you can find a complete course of linear algebra there.
Developing financial models
- Matrix theory combined with the theory of cost of capital made by Wong and Chan (2004). A pseudo-Bayesian model was made that defines investor behavior and market anomalies like under an overreaction, as well as market volatility.
- Matrix theory wad used for expanding capital cost theory for the time series model that provides dividends.
- Spectrum theory of larger dimensions any matrices and its uses to wireless communication and finance statistics
Creation of economic models:
- Lewis and Thorbecke in 1992 provided a finding of low regional social accounting matrix on district-level economic links of Kenya. The revenue relevancy is used for emphasizing sharing local economic effects of renewable energy projects. This feature is known as the social accounting approach.
- The social accounting method defines economics and conditions efficiency with the use of the theory of matrix.
- Masseti made a social entrepreneurship matrix like a “tipping point” for economic change.
- For the economics review of rheumatoid arthritis, a matrix of cost domains was given. Random matrix theory and the failure of macroeconomic projections were also introduced by Mounfield.
Creation of statistical models:
- Random matrix theory and universal statistics of chaotic quantum wires used random matrix theory chaotic quantum wires with spin-dependent hopping and the universal statistic.
- Searl used the algebra of matrices to help understand statistics.
- Andrew made spectral statistics with the use of the theory of large sample forms of matrices. It was developed by introducing spectrally right estimates.
- The stochastic dominance (SD) for averters and seekers has evolved and carries the concept of matrix theory concept to broaden SD checks for hazard averters and seekers.
- The SD theory for customers having reverse S-made application features increases and evolves through the concept of the matrices.
Applications of mathematical, economical, financial, and statistical models:
After the use of matrix theory for developing maths, economic and financial models then studied we can use models to analyze real-life problems.
- Such as after using random matrix theory for developing portfolio modeling models.
- There are some good uses of working after the application of the theory matrix such as production models, risk measures cointegration, and certain domains.
- For economical quality, it operated on technical analysis, trading features, and calendar anomalies.
- There are some other uses for financial stocks also. Such as warrant markets, stock markets, currencies and housing marketing.
Application of Matrix Theory in Education:
- Mathematical modeling features for high school teachers.
- Capacity of mathematical modeling for high school students.
- An effective way of teaching is through mathematical modeling.
Mathematical Modeling Steps:
- selection of unknown variables is our first step.
- Then select the condition for the variable.
- Solve the equation
- Checking the solution is also a compulsory step
Application of Matrix Theory in Reality:
The National Student Mathematics Olympiad is an important examination for university students in Vietnam because the contest gives a good working for students for learning and improves the teaching quality as well.
Practical mathematics problems in the national student mathematics Olympiad
Problem:
Let a and b be real numbers in any matrix A.
Solution:
- Find the determinant of A
- Compute A^-1
- A is invertible
- Find the values of a and b
Solving problems:
- Find determinant
- If a is not equal to b then A is invertible
- Then use the crammer rule
- Then apply a system of linear equations
- Then solve the equations
Conclusion:
So from the above discussion, the matrix theory plays a very important role in teaching mathematics and this theory is helpful in fields of economics, engineering, sciences finance, etc.
