03289nam 22005655 450 99641825910331620200810135051.0981-15-7261-510.1007/978-981-15-7261-6(CKB)4100000011384261(DE-He213)978-981-15-7261-6(MiAaPQ)EBC6299297(PPN)250213699(EXLCZ)99410000001138426120200810d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierFormalization of Complex Analysis and Matrix Theory[electronic resource] /by Zhiping Shi, Yong Guan, Ximeng Li1st ed. 2020.Singapore :Springer Singapore :Imprint: Springer,2020.1 online resource (X, 168 p. 357 illus.) 981-15-7260-7 Introduction -- Algebraic Systems -- Complex Numbers -- Gauge Integration -- FourierTransformation -- Discrete Fourier Transformation -- Matrices.This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.Applied mathematicsEngineering mathematicsComputer science—MathematicsApplications of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M13003Mathematical and Computational Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T11006Mathematics of Computinghttps://scigraph.springernature.com/ontologies/product-market-codes/I17001Applied mathematics.Engineering mathematics.Computer science—Mathematics.Applications of Mathematics.Mathematical and Computational Engineering.Mathematics of Computing.515Shi Zhipingauthttp://id.loc.gov/vocabulary/relators/aut1005287Guan Yongauthttp://id.loc.gov/vocabulary/relators/autLi Ximengauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996418259103316Formalization of Complex Analysis and Matrix Theory2311008UNISA