Abstract
In connection with tensors, matrices are of interest for two reasons.Firstly, they are tensors of order two and therefore a nontrivial example of a tensor.Differently from tensors of higher order, matrices allow us to apply practicallyrealisable decompositions. Secondly, operations with general tensors will often bereduced to a sequence of matrix operations (realised by well-developed software). Sections 2.1–2.3 introduce the notation and recall well-known facts about matrices. Section 2.5 discusses the important QR decomposition and the singular-valuedecomposition (SVD) and their computational cost. The (optimal) approximationby matrices of lower rank explained in Section 2.6 will be used later in truncationprocedures for tensors. In Part III we shall apply some linear algebra proceduresintroduced in Section 2.7 based on QR and SVD.
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Hackbusch, W. (2019). Matrix Tools. In: Tensor Spaces and Numerical Tensor Calculus. Springer Series in Computational Mathematics, vol 56. Springer, Cham. https://doi.org/10.1007/978-3-030-35554-8_2
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DOI: https://doi.org/10.1007/978-3-030-35554-8_2
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Print ISBN: 978-3-030-35553-1
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