Linear algebra

Fatemeh Hamidi Sepehr, Erchin Serpedin

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter will first review some basic concepts and results encountered in the study of vector spaces such as the notions of subspace, independence, basis, dimension, inner-product, norm and orthogonality, and then will focus on the general properties of linear transformations and matrix decompositions (LU, Cholesky, SVD and QR), and finally on various matrix operations and applications. This chapter represents a brief summary of the most important linear algebra concepts and results from the viewpoint of their applicability in the fields of signal processing, communications and networking. In writing this chapter, we made use of several excellent references available in the linear algebra literature [1-8]. For a more detailed description and additional topics, the readers are directed to these excellent references.

Original languageEnglish
Title of host publicationMathematical Foundations for Signal Processing, Communications, and Networking
PublisherCRC Press
Pages35-92
Number of pages58
ISBN (Electronic)9781439855140
ISBN (Print)9781138072169
DOIs
Publication statusPublished - 1 Jan 2017

Fingerprint

Linear algebra
Cholesky
Matrix Decomposition
Linear transformations
Singular value decomposition
Linear transformation
Vector spaces
Orthogonality
Networking
Scalar, inner or dot product
Vector space
Signal Processing
Signal processing
Subspace
Decomposition
Norm
Communication
Concepts
Independence
Review

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)
  • Engineering(all)

Cite this

Sepehr, F. H., & Serpedin, E. (2017). Linear algebra. In Mathematical Foundations for Signal Processing, Communications, and Networking (pp. 35-92). CRC Press. https://doi.org/10.1201/9781351105668

Linear algebra. / Sepehr, Fatemeh Hamidi; Serpedin, Erchin.

Mathematical Foundations for Signal Processing, Communications, and Networking. CRC Press, 2017. p. 35-92.

Research output: Chapter in Book/Report/Conference proceedingChapter

Sepehr, FH & Serpedin, E 2017, Linear algebra. in Mathematical Foundations for Signal Processing, Communications, and Networking. CRC Press, pp. 35-92. https://doi.org/10.1201/9781351105668
Sepehr FH, Serpedin E. Linear algebra. In Mathematical Foundations for Signal Processing, Communications, and Networking. CRC Press. 2017. p. 35-92 https://doi.org/10.1201/9781351105668
Sepehr, Fatemeh Hamidi ; Serpedin, Erchin. / Linear algebra. Mathematical Foundations for Signal Processing, Communications, and Networking. CRC Press, 2017. pp. 35-92
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