Linear algebra for multivariate methods

Subject description

Vector spaces

  • Eigenvalues and eigenvectors

  • Generalized inverses

  • Systems of linear equations

    Optional material:

  • Matrix factorizations and matrix norms

  • Partitioned matrices

  • Matrix derivatives

  • Quadratic forms

The subject is taught in programs

Objectives and competences

Student gets acquainted with linear algebra for use in statistics, especially in multivariat statistic methods.

Teaching and learning methods

Lectures, exercises, homeworks, projects, study of literature, consultations.

Expected study results

Knowledge and understanding:

  • vector spaces and matrices,

  • eigenvalues and eigenvectors,

  • inner product and adjacent matrices,

  • sebi-adjacent, pozitive definite, orthogonal in normal matrices,

  • generalized inverses,

  • solving systems of linear equations,

  • matrix factorizations,

  • matrix norms.

Basic sources and literature

J. R. Schott: Matrix analysis for statistics.

R. Horn, C. Johnson: Matrix analysis.

S. Lange: Linear algebra.

V. Omladič: Uporaba linearne algebre v statistiki.

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