METHOD FOR CALCULATING MATRIX RANK USING MODERN PROGRAMMING LANGUAGES
Keywords:
Matrix rank, linear algebra, NumPy library, Python programming, Flask web framework, matrix computation algorithm, interactive interface, programming in education, SVD (Singular Value Decomposition), system of linear equations.Abstract
This article focuses on an interactive application developed using Python and the Flask web framework for calculating the rank of a matrix. Matrix rank, a fundamental concept in linear algebra, represents the degree of linear independence of a matrix's rows or columns and is widely applied in areas such as linear systems, data compression, machine learning, and scientific research. The application enables users to input the dimensions and elements of a matrix, computes its rank using the NumPy library, and displays the result in a user-friendly interface. This tool is particularly beneficial in educational contexts for demonstrating linear algebra principles, as well as in research and practical applications that require efficient mathematical analysis. The article thoroughly explores the application's functionalities, technical structure, mathematical foundation, and practical significance, showcasing its role as a reliable and interactive computational resource for modern technological advancements.
In modern mathematics and technology, matrices occupy an important position, and their analytical and computational properties have become one of the main topics of fundamental research. Matrix color (rank) computation is important in various interdisciplinary studies, including linear algebra, differential equations, artificial intelligence algorithms, and data compression processes.
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References
Gilbert Strang, Linear Algebra and Its Applications, 4th Edition, Brooks Cole, 2005..
Refethen, Lloyd N., and David Bau III, Numerical Linear Algebra, SIAM, 1997.
NumPy Documentation: https://numpy.org/doc/
MATLAB Documentation: https://www.mathworks.com/help/matlab/
Julia Linear Algebra Documentation: https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/
Horn, Roger A., and Charles R. Johnson, Matrix Analysis, Cambridge University Press, 2012.
Golub, Gene H., and Charles F. Van Loan, Matrix Computations, Johns Hopkins University Press, 2013.
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