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Mathematische Werke. Mathematical works. Vol. 2: Linear algebra and analysis. Ed. by Bertram Huppert and Hans Schneider. (English, German) Zbl 0872.15004

Berlin: Walter de Gruyter. xx, 632 p. (1996).
This second volume of Helmut Wielandt’s collected mathematical works contains his contributions to linear algebra (including numerical and analytical theory of matrices) and to analysis.
Like the first volume (1994; Zbl 0802.20001) the book starts with Wielandt’s curriculum vitae, a list of his Ph.D. students and his acceptance of membership address to the Heidelberger Akademie der Wissenschaften. At the end of the book a complete bibliography of Wielandt’s published works is given.
The first main section of the volume contains about 24 research papers mostly on topics related to eigenvalues. To many of these papers commentaries are attached written by various contributors who were asked to remark also on recent developments of the topics under discussion.
The second main section contains the first printed version of the 1966/67 Madison lecture notes “Topics in the analytic theory of matrices” and also two commentaries. Since these lecture notes have become a standard reference in matrix theory, it is valuable that they are available now in print.
The third main section contains 7 reprints of mimeographed research reports of the Aerodynamische Versuchsanstalt Göttingen, containing also Wielandt’s contributions to the topic of inverse iteration in numerical mathematics.
The last section of the volume contains a collection of biographical notes (with respect to Issai Schur, Erhardt Schmidt and Hellmuth Kneser). As an appendix the lecture notes “Ausgewählte Fragen über Permutationsgruppen” follow which belong to the topics covered in the first volume but are here included for technical reasons.
The list of commenting contributors includes the names of Barker, Barnes, von Below, Bhatia, Brakhage, Brualdi, Davis, Fiedler, Friedland, Gustafson, Hoffman, Holbrook, Ipsen, Niethammer, Remmert, Schneider, Sun, Olga Taussky and Robert C. Thompson.

MSC:

15-03 History of linear algebra
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
01A75 Collected or selected works; reprintings or translations of classics
15A18 Eigenvalues, singular values, and eigenvectors
15A42 Inequalities involving eigenvalues and eigenvectors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
45D05 Volterra integral equations
65R20 Numerical methods for integral equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
20B07 General theory for infinite permutation groups

Citations:

Zbl 0802.20001

Software:

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