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Range Space and Similarity Transformation using Symbolic Mathematics in Python
  • Chainarong Wisassakwichai
Chainarong Wisassakwichai
Rajamangala University of Technology Krungthep

Corresponding Author:[email protected]

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Abstract

Linear systems involved in engineering and scientific calculations can be analyzed more easily using the mathematical tool of similarity transformation. However, understanding the numerous abstract linear algebra theorems associated with this transformation can be quite challenging. In this paper, we present computational methods for systematizing these theorems using SymPy (a symbolic mathematics library) in the Python programming language. The paper covers numerous theorems, including the basis of vector space, range space, null space, rank and nullity, eigenvalues, generalized eigenvectors, eigenspace, and diagonal-Jordan canonical form transformations. These theorems are transformed into abstract data models, which are then represented as programmatic objects using Object-Oriented Programming (OOP) for processing input and output data. The aim of this paper is to provide a more efficient and effective means of displaying and applying these theorems through the use of computers. A Python programming language module was eventually created from the developed programmatic objects. It can be used for programming both offline on PC and online through the web application “SymPy Live,” producing satisfactory computational results compared to MATLAB, even when used on mobile devices.