Collected Mathematical Papers: Vol. 1 I Determinants II Linear Algebra III Algebraic Equations

by A. Ostrowski

Overview

This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen tiber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhiiuser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhiiuser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York (1973); and Stu­ dien tiber den Schottkyschen Satz (Studies on Schottky's Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conclusion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper. (There is one exception: the correc­ tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication.

Product Details

ISBN-13:	9783034893572
Publisher:	Birkhäuser Basel
Publication date:	11/15/2011
Edition description:	Softcover reprint of the original 1st ed. 1983
Pages:	904
Product dimensions:	6.69(w) x 9.61(h) x 0.07(d)

Table of Contents

I Determinants.- 86 Sur la détermination des bornes inférieures pour une classe des déterminants, Bull. Sc. Math. (2) 61, 1–14 (1937).- 87 Über die Determinanten mit überwiegender Hauptdiagonale, Comment. Math. Helv. 10, 69–96 (1937).- 95 Sur l’approximation du déterminant de Fredholm par les déterminants des systèmes d’équations linéaires, Ark. Mat. Skholm 26A, 1–15 (1938).- 129 (With Olga Taussky) On the Variation of the Determinant of a Positive Definite Matrix, Nederl. Indag. Math. 13, 383–385 (1951).- 131 Note on Bounds for Determinants with Dominant Principal Diagonal, Proc. Amer. Math. Soc. 3, 26–30 (1952).- 148 Note on Bounds for some Determinants, Duke Math. J. 22, 95–102(1955).- 155 Sur les déterminants à diagonale dominante, Bull. Soc. Math. Belg. 46–51 (1954).- 191 On some Conditions for Nonvanishing of Determinants, Proc. Amer. Math. Soc. 12, 268–273 (1961).- 194 Über geränderte Determinanten und bedingte Trägheitsindizes quadratischer Formen, Monatsh. Math. 64, 51–63 (1960).- 211 On some Determinants with Combinatorial Numbers (Dedicated to Helmut Hasse for his 65th birthday), J. f. d. r. u. angew. Math. 216, 25–30(1964).- II Linear Algebra.- 96 On a Theorem Concerning Identical Relations between Matrices, Quart. J. Math., Oxford Ser. 9, 241–245 (1938).- 119 Sur la variation de la matrice inverse d’une matrice donnée, C.R. Acad. Sc. Paris 231, 1–3 (1950).- 127 Über das Nichtverschwinden einer Klasse von Determinanten und die Lokalisierung der charakteristischen Wurzeln von Matrizen, Comp. Math. 9, 209–226 (1951).- 128 Sur les conditions générates pour la régularité des matrices, R. C. Mat. eappl. (5) 10, 156–168 (1951).- 132 Bounds for the Greatest Latent Root of a Positive Matrix, J.L.M.S. 27, 253–256(1952).- 143 On the Linear Iteration Procedures for Symmetric Matrices (In memory of Fabio Conforto), R.C. Mat. e appl. (5) 13, 140–163 (1954).- 144 On the Spectrum of a One-Parametric Family of Matrices, J. f. d. r. u. angew. Math. 193, 143–160 (1954).- 153 Über Normen von Matrizen (Dem Andenken an Issai Schur gewidmet), Math. Z. 63, 2–18 (1955).- 171 Mathematische Miszellen. XXVII. Über die Stetigkeit von charakteristischen Wurzeln in Abhängigkeit von den Matrizenelementen, Jber. Deutsch. Math.-Verein. 60, 40–42 (1957).- 174 On the Convergence of the Rayleigh Quotient Iteration for the Computation of the Characteristic Roots and Vectors. I, Arch. Rational Mech. An. 1, 233–241 (1958).- 176 On the Bounds of a One-Parametric Family of Matrices, J. f. d. r. u. angew. Math. 200, 190–199 (1958).- 178 On the Convergence of the Rayleigh Quotient Iteration for the Computation of the Characteristic Roots and Vectors. II, Arch. Rational Mech. An. 2, 423–428 (1959).- 183 Über Eigenwerte von Produkten Hermitescher Matrizen (Helmut Hasse zum 60. Geburtstag), Hamburger Abh. 23, 60–68 (1959).- 185 A Quantitative Formulation of Sylvester’s Law of Inertia, Proc. Nat. Acad. Sc. U.S.A. 45, 740–744 (1959).- 186 On the Convergence of the Rayleigh Quotient Iteration for the Computation of the Characteristic Roots and Vectors. Ill (Generalized Rayleigh Quotient and Characteristic Roots with Linear Elementary Divisors), Arch. Rational Mech. An. 3, 325–340 (1959).- 187 On the Convergence of the Rayleigh Quotient Iteration for the Computation of the Characteristic Roots and Vectors. IV (Generalized Rayleigh Quotient for Nonlinear Elementary Divisors), Arch. Rational Mech. An. 3, 341–347 (1959).- 188 On the Convergence of the Rayleigh Quotient Iteration for the Computation of the Characteristic Roots and Vectors. V (Usual Rayleigh Quotient for Non-Hermitian Matrices and Linear Elementary Divisors), Arch. Rational Mech. An. 3, 472–481 (1959).- 189 On the Convergence of the Rayleigh Quotient Iteration for the Computation of Characteristic Roots and Vectors. VI (Usual Rayleigh Quotient for Nonlinear Elementary Divisors), Arch. Rational Mech. An. 4, 153–165 (1959).- 190 Über Produkte Hermitescher Matrizen und Büschel Hermitescher Formen (Dem Andenken an Leon Lichtenstein gewidmet), Math. Z. 72, 1–15 (1959).- 192 A Regularity Condition for a Class of Partitioned Matrices, Comp. Math. 15, 23–27 (1962).- 193 On the Convergence of Gauss’ Alternating Procedure in the Method of the Least Squares (A Giovanni Sansone nel suo 70. compleanno), Ann. Mat. pura appl. (4) 48, 229–235 (1959).- 196 On the Eigenvector Belonging to the Maximal Root of a Non-negative Matrix, Proc. Edinburgh Math. Soc. (2) 12, 107–112 (1960–1961).- 198 A Quantitative Formulation of Sylvester’s Law of Inertia, II, Proc. Nat. Acad. Sc. U.S.A. 46, 859–862 (1960).- 201 (With Hans Schneider) Bounds for the Maximal Characteristic Root of a Non-Negative Irreducible Matrix, Duke Math. J. 27, 547–553 (1960).- 202 Note on a Theorem by Hans Schneider, J.L.M.S. 37, 225–234 (1962).- 203 On Some Inequalities in the Theory of Matrices (Dedicated to the memory of Jekuthiel Ginsburg), Scripta Math. 26, 201–222 (1963).- 205 (With Hans Schneider) Some Theorems on the Inertia of General Matrices, J. Math. An. Appl. 4, 72–84(1962).- 206 On Positive Matrices (To B.L. van der Waerden for his 60th anniversary), Math. Ann. 150, 276–284 (1963).- 208 Il metodo del quoziente di Rayleigh, (C.I.M.E., Roma), 1–60 (1963).- 215 Positive Matrices and Functional Analysis in Recent Advances in Matrix Theory (Univ. Wisconsin Press, Madison, Wisconsin), 81–101 (1964).- 227 (With E.V. Haynsworth) On the Inertia of Some Classes of Partitioned Matrices, Lin. Alg. a. Appl. 1, 299–316 (1968).- 237 A New Proof of Haynsworth’s Quotient Formula for Schur Complements (Dedicated to the memory of Theodore S. Motzkin), J. Comb. Theory 14, 389–392 (1973).- 243 On Schur’s Complement (Dedicated to the memory of Theodore S. Motzkin), J. Comb. Theory 14, 319–323 (1973).- 245 On Subdominant Roots of Non-Negative Matrices, Lin. Alg. a. Appl. 8, 179–184(1974).- III Algebraic Equations.- 21 Notiz über einen Satz der Galoisschen Theorie, Math. Z. 12, 317–322(1922).- 48 Mathematische Miszellen. XII. Bemerkungen zum Beweise des Budan-Fourierschen und Newton-Sylvesterschen Satzes, Jber. Deutsch. Math.-Verein. 37, 254–256 (1928).- 66 Über den ersten und vierten Gausschen Beweis des Fundamental-satzes der Algebra, in C.F. Gauss Werke, X (Springer Verlag, Berlin), 3-18 (1933).- 68 (Mit Th. Motzkin) Über den Fundamentalsatz der Algebra, S.-B. Berlin Akad., 1–4 (1933).- 97 Sur la continuité relative des racines d’équations algébriques, C.R. Acad. Sc. Paris 209, 1–3 (1939).- 100 Recherches sur la méthode de Graeffe et les zéros des polynomes et des séries de Laurent, Acta Math. 72, 99–257 (1940).- 100a Addition à notre mémoire: Recherches sur la methode de Graeffe et les zéros des polynomes et des séries de Laurent, Acta Math. 75, 183–186(1943).- 104 On a Theorem by J. L. Walsh Concerning the Moduli of Roots of Algebraic Equations, Bull. A.M.S. 47, 742–746 (1941).- 121 Note on Vincent’s Theorem, Ann. of Math. 52, 702–707(1950).- 124 Sur une règie de Laguerre, Ann. Mat. pura appl. (4) 31, 65–68 (1950).- 154 Note on a Theorem by A. Brauer, Duke Math. J. 22, 469–470 (1955).- 159 Mathematische Miszellen. XXIV. Zur relativen Stetigkeit von Wurzeln algebraischer Gleichungen, Jber. Deutsch. Math.-Verein. 58,98–102(1956).- 164 Über die Darstellung von symmetrischen Funktionen durch Potenzsummen, Math. Ann. 132, 362–372 (1956).- 182 Über einige Sätze von Herrn M. Parodi (Dem Andenken an H.L. Schmid), Math. Nachr. 19, 331–338 (1958).- 199 On the Zeros of Bernoulli Polynomials of Even Order, Enseignement Math. 6, 27–47 (1960).- 200 On an Inequality of J. Vicente Gonçalves, Univ. Lisboa Rivista Fac. Ci. A (2) 8, 115–119(1961).- 207 Eine Vorzeichenregel in der Theorie der algebraischen Gleichungen, von Carl Runge, herausgegeben von A. Ostrowski, Jber. Deutsch. Math.-Verein. 66, 52–66 (1963).- 209 Sur l’analogue du théorème de Budan-Fourier pour les suites générates des polynomes, J. Math, pures appl. (9) 43, 49–58 (1964).- 210 On Runge’s General Rule of Signs, Ann. Ac. Sc. Fenn. (A) I 342, 3–20(1964).- 214 On Descartes Rule of Signs for Certain Polynomial Developments (To G. Pólya for his 70th anniversary), J. Math. Mech. 14, 195–209 (1965).- 217 Note sur les parties réelles et imaginaires des racines des polynomes, J. Math, pures appl. (9) 44, 327–329 (1965).- 220 Sur une propriété des sommes des racines d’un polynome, C.R. Acad. Sc. Paris 263, 46–48 (1966).- 224 On the Moduli of Zeros of Derivatives of Polynomials, J. f. d. r. u. angew. Math. 230, 40–50 (1968).- 234 A Theorem on Clusters of Roots of Polynomial Equations (To A. S. Householder for his 65th birthday), SIAM J. Num. An. 7, 567–570(1970).- 238 Some Properties of Reduced Polynomial Equations, SIAM J. Num. An. 8,623–638 (1971).- 250 On Subdominant Roots of Certain Algebraic Equations (Papers dedicated to L. Iliev’s 60th anniversary), Mathematical Structures, 383–386 (Sofia, 1975).- 263 Notiz über Maximalwerte von Polynomen auf dem Einheitskreis (To the 70th birthday of E. Lucacs), Elektrotechn. Fak. Belgrad, 55/56 (1979).- Vol. 1–6.- Collected Mathematical Papers ordered chronologically according to the date of original publication.