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2007•Society for Industrial and Applied Mathematics eBooksRequires access

5. QR Decomposition

Lars Eldén

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Abstract

One of the main themes of this book is decomposition of matrices to compact (e.g., triangular or diagonal) form by orthogonal transformations. We will now introduce the first such decomposition, the QR decomposition, which is a factorization of a matrix A in a product of an orthogonal matrix and a triangular matrix. This is more ambitious than computing the LU decomposition, where the two factors are both required only to be triangular.

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One of the main themes of this book is decomposition of matrices to compact (e.g., triangular or diagonal) form by orthogonal transformations. We will now introduce the first such decomposition, the QR decomposition, which is a factorization of a matrix A in a product of an orthogonal matrix and a triangular matrix. This is more ambitious than computing the LU decomposition, where the two factors are both required only to be triangular.

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Available abstract

One of the main themes of this book is decomposition of matrices to compact (e.g., triangular or diagonal) form by orthogonal transformations. We will now introduce the first such decomposition, the QR decomposition, which is a factorization of a matrix A in a product of an orthogonal matrix and a triangular matrix. This is more ambitious than computing the LU decomposition, where the two factors are both required only to be triangular.

Key concepts: Triangular matrix, QR decomposition, Orthogonal matrix, Mathematics, LU decomposition, Matrix decomposition, Diagonal, Matrix (chemical analysis)

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