Enhancing JMatrix with additional methods

[mitsuki31]

Requested Feature

JMatrix, an educational Java library designed to simplify matrix operations, aims to provide a comprehensive learning tool for high school students exploring linear algebra concepts. To further enhance its usability and support a broader range of learning scenarios, the addition of certain methods is recommended. These methods will allow students or users to explore and understand specific matrix properties and operations more effectively.

• trace, introduced in New matrix operations and helper APIs #102
• determinant introduced in feat: Add support for determinant calculation #131
• isSparse, introduced in New matrix operations and helper APIs #102
• isPermutationMatrix introduced in feat: Enhance Matrix class with row/column getters and permutation matrix checks #134

Description of Proposed Methods

• trace
  The trace of a square matrix is the sum of its diagonal elements. It is a valuable property used in various matrix-related calculations. The trace method will allow users to obtain the trace of square matrices, providing insights into matrix characteristics and operations.

• determinant
  The determinant of a square matrix is a fundamental property that holds valuable information about the matrix's invertibility and scaling factor of transformations. Adding the determinant method to JMatrix will empower users to compute determinants of square matrices, fostering a deeper understanding of matrix properties.

• isSparse
  A matrix is considered sparse if the majority of its elements are zero. For large matrices with a significant number of zeros, sparse matrix representation can offer substantial memory and computation efficiency. The isSparse method will help users to identify whether a matrix is sparse, making it easier to recognize opportunities for utilizing sparse matrix algorithms.

• isPermutationMatrix
  A permutation matrix is a square binary matrix that represents a permutation of the rows or columns of an identity matrix. It has exactly one $1$ in each row and each column, with all other elements being zeros. The isPermutationMatrix method will allow users to check if a given square matrix is a permutation matrix, aiding in the study of permutation-based operations.

Issue Summary

This issue aims to enrich the JMatrix library by adding several essential methods that will enhance the learning and application of linear algebra concepts. The proposed methods cover various aspects of matrix analysis, including determining permutation matrices, recognizing sparse matrices, and calculating determinant and trace. By implementing these methods, JMatrix will become an even more valuable educational resource, providing comprehensive support for users exploring linear algebra concepts.

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