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2013•Unpublished venueRequires access

Linear Algebra

Petre P. Teodorescu, Nicolae–Doru Stănescu, Nicolae Pandrea

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Abstract

This chapter on linear algebra first discusses calculation of determinants and rank, norm of a matrix, and inversion of matrices. Next, it deals with solution of linear algebraic systems of equations. Then, it gives definitions of QR decomposition and the singular value decomposition (SVD). The use of the least squares method in solving the linear overdetermined systems, the pseudo-inverse of a matrix, and solving of the underdetermined linear systems are considered. These are followed by applications.

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What this paper is about

This chapter on linear algebra first discusses calculation of determinants and rank, norm of a matrix, and inversion of matrices. Next, it deals with solution of linear algebraic systems of equations. Then, it gives definitions of QR decomposition and the singular value decomposition (SVD). The use of the least squares method in solving the linear overdetermined systems, the pseudo-inverse of a matrix, and solving of the underdetermined linear systems are considered. These are followed by applications.

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Available abstract

This chapter on linear algebra first discusses calculation of determinants and rank, norm of a matrix, and inversion of matrices. Next, it deals with solution of linear algebraic systems of equations. Then, it gives definitions of QR decomposition and the singular value decomposition (SVD). The use of the least squares method in solving the linear overdetermined systems, the pseudo-inverse of a matrix, and solving of the underdetermined linear systems are considered. These are followed by applications.

Key concepts: Overdetermined system, Underdetermined system, Singular value decomposition, Linear algebra, Mathematics, Algebra over a field, System of linear equations, QR decomposition

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