Matrix algebra

H. Yanai, H. Ishii

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Definition and basic operations of matrices are described. Fundamental properties of matrices such as rank, determinants, inverse, and positive (semi)definiteness are also identified. Eigenvalues and eigenvectors, spectral and singular value decompositions are described with numerical examples. Projection matrices, generalized inverse of a matrix, Kronecker product, and Vec operator are briefly explained. Basic applications of matrix algebra to multivariate analysis, a correlation matrix, and principal-component analyses are provided.

Original languageEnglish
Title of host publicationInternational Encyclopedia of Education
PublisherElsevier Ltd
Pages253-259
Number of pages7
ISBN (Print)9780080448947
DOIs
Publication statusPublished - 01-12-2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance(all)

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  • Cite this

    Yanai, H., & Ishii, H. (2010). Matrix algebra. In International Encyclopedia of Education (pp. 253-259). Elsevier Ltd. https://doi.org/10.1016/B978-0-08-044894-7.01341-5