### 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 language | English |
---|---|

Title of host publication | Mathematical Foundations for Signal Processing, Communications, and Networking |

Publisher | CRC Press |

Pages | 35-92 |

Number of pages | 58 |

ISBN (Electronic) | 9781439855140 |

ISBN (Print) | 9781138072169 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)
- Engineering(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Mathematical Foundations for Signal Processing, Communications, and Networking.*CRC Press, pp. 35-92. https://doi.org/10.1201/9781351105668

}

TY - CHAP

T1 - Linear algebra

AU - Sepehr, Fatemeh Hamidi

AU - Serpedin, Erchin

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

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U2 - 10.1201/9781351105668

DO - 10.1201/9781351105668

M3 - Chapter

SN - 9781138072169

SP - 35

EP - 92

BT - Mathematical Foundations for Signal Processing, Communications, and Networking

PB - CRC Press

ER -