Chapter: Introduction to Matrices and Vectors

Matrices and vectors are interesting mathematical objects on their own. They are frequently used in the linear algebra in many other mathematical disciplines. While we will study their properties later in more detail, in this section we shall limit ourselves to some basic definitions and notations needed to proceed with our study of systems of linear equations.

  1. Definition: Matrix, Set of Matrices over a Field
  2. Definition: Transposed Matrix
  3. Definition: Column Vectors and Row Vectors
  4. Section: Addition of Matrices and Vectors
  5. Definition: Square Matrix
  6. Definition: Matrix Multiplication
  7. Definition: Identity Matrix
  8. Definition: Invertible and Inverse Matrix

Chapters: 1

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  1. Knabner, P; Barth, W.: "Lineare Algebra - Grundlagen und Anwendungen", Springer Spektrum, 2013