Appendix C: Facts from Hilbert Space Theory

Giorgio Picci
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Giorgio Picci: University of Padua, Department of Information Engineering

Chapter 12 in An Introduction to Statistical Data Science, 2024, pp 419-428 from Springer

Abstract: Abstract A Hilbert space is a vector space with an inner product ( H , 〈 ⋅ , ⋅ 〉 ) $$(\mathbf H,\langle \,\cdot \,,\,\cdot \,\rangle )$$ which is complete with respect to the metric induced by the inner product. In other words, every Cauchy sequence has a limit in H $$\mathbf H$$ . To establish notation, we shall give examples of Hilbert spaces which are used in this book.

Date: 2024
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DOI: 10.1007/978-3-031-66619-3_12

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