CaltechAUTHORS: Article
https://feeds.library.caltech.edu/people/Taussky-Todd-O/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 21 May 2024 19:52:12 -0700Beiträge zur Funktionentheorie in nichtarchimedisch bewerteten Körpern
https://resolver.caltech.edu/CaltechAUTHORS:20201016-125822442
Year: 1931
DOI: 10.1007/bf01700786
Book review of:
W. Schöbe, (Universitätsarchiv Bd. 42; zugleich Mathematische Abteilung Bd. 2, herausgeg. von H. Hasse). 61 Seiten. Helios-Verlag G. m. b. H., Münster i. W. 1930. Preis geh. RM 6https://resolver.caltech.edu/CaltechAUTHORS:20201016-125822442Moderne Algebra [book review]
https://resolver.caltech.edu/CaltechAUTHORS:20201016-125822612
Year: 1932
DOI: 10.1007/bf01699101
Review of:
B. L. van der Waerden, (Unter Benützung von Vorlesungen von E. Artin und E. Noether.) I. Teil. (Die Grundlehren der mathematischen Wissenschaften, Band XXXIII.) J. Springer, Berlin 1930. VIII und 243 S. Preis geh. RM 15,60, geb. RM 17,20https://resolver.caltech.edu/CaltechAUTHORS:20201016-125822612Gesammelte mathematische Werke [Book review]
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905755
Year: 1932
DOI: 10.1007/bf01699097
Richard Dedekind, Herausgegeben von R. Fricke, E. Noether, Ö. Ore. II. Band. 442 Seiten. Friedrich Vieweg & Sohn, Braunschweig 1931. Preis geh. RM 40,50, geb. 43https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905755Einführung in die Zahlentheorie
https://resolver.caltech.edu/CaltechAUTHORS:20201015-152734918
Year: 1933
DOI: 10.1007/bf01708886
Book review of:
Einführung in die Zahlentheorie
L. E. Dickson — E. Bodewig. B. G. Teubner, Leipzig 1931. Preis geb. RM 9,60https://resolver.caltech.edu/CaltechAUTHORS:20201015-152734918Moderne Algebra [Book review]
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905919
Year: 1933
DOI: 10.1007/bf01708891
B. L. van der Waerden. Bd. II. (Grundlehren der mathematischen Wissenschaft in Einzeldarstellungen. Bd. 34.) J. Springer, Berlin 1931. Preis geb. RM 15,-https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905919R. Dedekind, Gesammelte mathematische Werke
https://resolver.caltech.edu/CaltechAUTHORS:20201015-152734797
Year: 1933
DOI: 10.1007/bf01708918
Book review: R. Dedekind, Gesammelte mathematische Werke
Bd. 3. F. Vieweg u. S., Braunschweig 1932. Preis geh. RM 41,40https://resolver.caltech.edu/CaltechAUTHORS:20201015-152734797Über isomorphe Abbildungen von Gruppen
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100906020
Year: 1933
DOI: 10.1007/bf01452855
[no abstract]https://resolver.caltech.edu/CaltechAUTHORS:20201022-100906020Characteristic roots of quaternion matrices
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905650
Year: 1954
DOI: 10.1007/bf01899323
In two recent publications [1], [2] it was shown that for matrices of (real) quaternion elements an eigenvalue theory can be developed similar to that for complex numbers. If A is such a matrix then quaternion elements λ and quaternion vectors x can be found such that Ax = xλ.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905650Discrete analogs of inequalities of Wirtinger
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905487
Year: 1955
DOI: 10.1007/bf01302991
In the theory of inequalities there are often encountered inequalities which are first proved for finite series and then established for infinite series or integrals. We shall discuss here the finite analogs of several integral inequalities which appear to have been established directly. There is often the added interest in the finite case of considering whether or not an improvement in the constants is possible (cf. H. Frazer [7]).https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905487Unimodular integral circulants
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905336
Year: 1955
DOI: 10.1007/bf01187938
Some properties of the "discriminant matrix" (α_i^(S_k))) of a normal algebraic number field of degree n were investigated in two previous notes (1 ,2). Here the α_i form an integral basis of the field and the S_k are the elements of the GALOIS group). In the special case when the α_i form a normal basis various problems concerning group matrices arise, among others, questions concerning unimodular group matrices whose elements are rational integers. If the field is cyclic circulant, matrices appear, i.e. matrices C = (c_(ik)) with c_(ik) = c_(k-i+1) where the suffixes are considered mod n. In particular the following theorem was obtained which will be studied further in the present note.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905336A weak property L for pairs of matrices
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905183
Year: 1959
DOI: 10.1007/bf01181419
A pair of n x n matrices A, B with complex numbers as elements is said to have the L-property if λA + µB has as characteristic roots λα_i + µβ_i, where α_i are the characteristic roots of A and β_i the characteristic roots of B--taken in a special ordering--and when λ,µ run through all complex numbers. Let one of the matrices, say A, be diagonable (i.e. similar to a diagonal matrix). The following condition on B is then necessary for A and B to have property L (see T. S. MOTZKIN and O. TAUSSKY [1] p. 108--109).https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905183Some remarks concerning the real and imaginary parts of the characteristic roots of a finite matrix
https://resolver.caltech.edu/CaltechAUTHORS:LEWjmp60
Year: 1960
DOI: 10.1063/1.1703658
Some theorems are obtained on the existence of certain determinantal equations whose roots are separately the real or imaginary parts of the characteristic roots of a given matrix with simple elementary divisors. When the elementary divisors are not simple, similar, but somewhat less precise, results are obtained.https://resolver.caltech.edu/CaltechAUTHORS:LEWjmp60On the theory of orders, in particular on the semigroup of ideal classes and genera of an order in an algebraic number field
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905016
Year: 1962
DOI: 10.1007/bf01438389
The study of fractional ideals of orders of algebraic number fields and their equivalence is closely related to the study of matrices with rational integral elements and their similarities under unimodular transformations.
Such a study should at some stage proceed to the inspection of actual numerical examples. However, quite simple questions, such as the problem of the arithmetical equivalence of two ideals with the same order (see below), require a large number of computational steps. Therefore this task calls for the use of automatic highspeed computers.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100905016Ideal matrices. I
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904906
Year: 1962
DOI: 10.1007/bf01650074
By an ideal matrix is understood a square matrix of rational integers which transforms a basis for the integers of an algebraic number field into a basis for an ideal in this ring. The same term will be used also for the analogous relation in an order of such a field. (This concept was studied by MACDUFFEE [1], for associative algebras over the rationals, later for abstract associative algebras [2]; it goes back to Poincaré [3], [4] and CHÂTELET [5]).
In this note two aspects of ideal matrices are studied:
1) Ideal matrices and their connection with classes of matrices.
2) For what kind of number field is a given non-singular square matrix of rational integers an ideal matrix?https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904906Ideal matrices II
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904791
Year: 1963
DOI: 10.1007/bf01396991
In order to make this paper self-contained the definition of ideal matrix is repeated. It is a square matrix of rational integers which transforms a basis for the integers of an algebraic number field (or of an order in such a field) into a basis for an ideal.
The aim of this paper is to describe such a matrix from the prime ideal factorization of the corresponding ideal.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904791On the similarity transformation between an integral matrix with irreducible characteristic polynomial and its transpose
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904669
Year: 1966
DOI: 10.1007/bf01361438
Let A and S be matrices of rational integers and let A have
a characteristic polynomial f which is irreducible over the rationals. Let (1) S⁻¹AS = A'.
A great deal can be said about the structure of all possible S's. In first place S is symmetric by an earlier result of H. ZASSENHAUS and O. TAUSSKY [3]. In 2. an explicit expression for S will be given which is already contained in
FADDEEV [2], TAUSSKY [4], BENDER [1]. In 3. the determinant of S is discussed. In 4. a fractional ideal associated with the set of all solutions of (1) is constructed.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904669Remarks on a matrix theorem arising in statistics
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904530
Year: 1966
DOI: 10.1007/bf01300451
The following Theorem 1. plays a certain role in statistics and proofs and generalizations have appeared for some time (for algebraic proofs and references see [l], [2]). Although the matrices studied in the theorem are finally shown to be commutative the proofs so far do not go after this fact explicitly. Here a proof wiU be given which links the theorem with commutativity. Further, a recently obtained generalization of the theorem is reproved by reducing it to the special case.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904530On the l-cohomology of the general and special linear group l
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904390
Year: 1969
DOI: 10.1007/bf01817525
The functional equation f(ab) = f(a) + af(b) (1) is discussed. It arises in connection with the 1-cohomology. Here the case of the general linear group or the special linear group over a field F acting as inner automorphisms on the full matrix algebra of the same degree or the stable subspace of matrices of trace zero is treated.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904390A remark concerning the similarity of a finite matrix A and A*
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904269
Year: 1970
DOI: 10.1007/bf01109842
Such a transformation always exists if A is real. For a complex matrix A it exists only if A is similar to a real matrix (see, e.g. [3]).https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904269On the 1-cohomology of the general and special linear groups
https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904052
Year: 1970
DOI: 10.1007/bf01818441
In this paper we discuss the functional equation f(ab) = f(a) + a(f(b)) which arises in connection with the l-cohomology of the general linear group over a
field F acting as inner automorphisms on the full matrix algebra of the same degree.https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904052Norms in quadratic fields and their relations to non commuting 2×2 matrices I
https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023229
Year: 1976
DOI: 10.1007/bf01526330
Let A be a fixed 2×2 integral matrix with irrational characteristic roots. Let B be an arbitrary 2×2 integral matrix. It was previously shown that -det (AB-BA) = norm λ, where λ is in the field of the characteristic roots of A. It is now shown that the λ's corresponding to varying B's can be chosen to form a fractional ideal in this field.https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023229Norms from quadratic fields and their relation to noncommuting 2×2 matrices III. A link between the 4-rank of the ideal class groups in ℚ(√m) and in ℚ(√-m)
https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023016
Year: 1977
DOI: 10.1007/bf01241822
This paper is concerned with the representation of an integral 2 x 2 matrix A as A = S₁S₂ with S_i = S'_i and integral and facts connected with it.
In [6] the following was shown. If the characteristic polynomial of A is
x²-m with m square free and ≡2 or 3(4) then a factorization of A as above is only
possible if the ideal class in Z[√m[ associated with A is of order a factor of 4. If
the ideal class is of order 4 then the S_i cannot be unimodular.
Now it is shown that a factorization for an A with characteristic polynomial
x²-m, m square free, leads to an ideal class in the narrow sense of order 4 in
Z[√-m]. This is achieved by associating with the factorization an integral
ternary form representing zero in a nontrivial way. The conditions for this to
happen are known.https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023016Ideal matrices. III.
https://resolver.caltech.edu/CaltechAUTHORS:TAUpjm85
Year: 1985
In this paper ideal matrices with respect to ideals in the maximal order of an algebraic number field are connected with the different of the field and with group matrices in the case of normal fields whose maximal order has a normal basis.https://resolver.caltech.edu/CaltechAUTHORS:TAUpjm85