Linear Algebra

Massimiliano Porto
Additional contact information
Massimiliano Porto: Kobe University

Chapter Chapter 2 in Introduction to Mathematics for Economics with R, 2022, pp 55-241 from Springer

Abstract: Abstract The first part of the chapter focuses on vectors (Sect. 2.2) and matrices (Sect. 2.3). In particular, we will cover vector space (Sect. 2.2.1), operations with vectors and matrices, linear independence (Sect. 2.2.8), systems of linear equations (Sect. 2.3.7), and the determinant (Sect. 2.3.8). In the second part of the chapter, we will learn topics such as eigenvalues and eigenvectors (Sect. 2.3.9), diagonalization process (Sect. 2.3.9.1), and definiteness of matrices (Sect. 2.3.12). Section 2.3.13 introduces to matrix decomposition. We will see examples of Spectral decomposition, Singular Value Decomposition, Cholesky decomposition and QR decomposition. Applications in Economics include: the budget set, the IS-LM model, the Leontief Input-Output model, Network analysis and linear model. Examples of functions coded from scratch include functions to compute the determinant with the Laplace expansion method and with the eigenvalues, a function to compute the unit vector, a function to compute the inner product, a function to compute the leading principal minors.

Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-05202-6_2

Ordering information: This item can be ordered from
http://www.springer.com/9783031052026

DOI: 10.1007/978-3-031-05202-6_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().