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Arrays and Linear Algebra

In: Algorithms with JULIA

Author

Listed:
  • Clemens Heitzinger

    (Technische Universität Wien, Center for Artificial Intelligence and Machine Learning (CAIML) and Department of Mathematics and Geoinformation)

Abstract

Arrays are a multi-dimensional data structure and hence encompass the mathematical structures of vectors, matrices, and tensors. An important application of arrays is the numerical implementation of linear algebra. In certain applications, the majority of the entries of vectors or matrices are zero; in these situations, the sparse versions should be used instead of the dense ones. Operations on dense and sparse arrays are discussed in detail in this chapter, including those from linear algebra such as solving systems of linear equations, calculating the eigenvalues and eigenvectors of matrices, singular-value decomposition, and matrix factorizations.

Suggested Citation

  • Clemens Heitzinger, 2022. "Arrays and Linear Algebra," Springer Books, in: Algorithms with JULIA, chapter 0, pages 153-226, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-16560-3_8
    DOI: 10.1007/978-3-031-16560-3_8
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