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2 results

  • 2 - Introduction to Matrices

  • Jeffrey A. Fessler, University of Michigan, Ann Arbor, Raj Rao Nadakuditi, University of Michigan, Ann Arbor
  • Book:
    Linear Algebra for Data Science, Machine Learning, and Signal Processing
    Published online:
    01 November 2024
    Print publication:
    16 May 2024, pp 12-62

  • Summary

    This chapter reviews vectors and matrices, and basic properties like shape, orthogonality, determinant, eigenvalues, and trace. It also reviews operations like multiplication and transpose. These operations are used throughout the book and are pervasive in the literature. In short, arranging data into vectors and matrices allows one to apply powerful data analysis techniques over a wide spectrum of applications. Throughout, this chapter (and book) illustrates how the ideas are implemented in practice in Julia.

  • 2 - Matrix Algebra

  • David C. Vella, Skidmore College, New York
  • Book:
    Invitation to Linear Programming and Game Theory
    Published online:
    11 March 2021
    Print publication:
    11 March 2021, pp 63-101

  • Summary

    This chapter provides a basic introduction to matrices, including the following: scaling, transposing, adding, and subtracting matrices; multiplying matrices and applications; finding determinants and inverses of 2 x 2 matrices; and solving systems of equations by matrix inversion. Applications of matrix algebra, including applications to cryptography and to Leontief economic models, are discussed.A method for finding inverses of larger matrices using elimination is developed in a series of exercises.