

Bibliography for
Quaternions
unabridged
- Passive Attitude Control of Flexible Spacecraft from
Quaternion Measurements
Di Gennaro S.
Journal of Optimization Theory and Applications, January 2003,
vol. 116, no. 1, pp. 41-60(20), Ingenta.
- GPS-based attitude determination of gyrostat satellite by
quaternion estimation algorithms
Kuang J.; Tan S.
Acta Astronautica, November 2002, vol. 51, no. 11, pp.
743-759(17), Ingenta.
- Pressure Transmitter Surveillance Using Quaternion Numbers
Chicharro J.M.; García-Berrocal A.; Balbás M.;
Bla´Zquez J.
Mechanical Systems and Signal Processing, November 2002, vol. 16,
no. 6, pp. 1083-1091(9), Ingenta.
- Fast Quaternion Attitude Estimation from Two Vector
Measurements
Markley F.L.
Journal of Guidance, Control, and Dynamics, 1 March 2002, vol. 25,
no. 2, pp. 411-414(4), Ingenta.
- An Analog of the Poincaré Model for a Quaternion
Hyperbolic Space
Volchkov V.V.
Ukrainian Mathematical Journal, October 2001, vol. 53, no. 10, pp.
1618-1625(8), Ingenta.
- Quaternion-Based Adaptive Attitude Tracking Controller Without
Velocity Measurements
Costic B. T.; Dawson D. M.; de Queiroz M. S.; Kapila V.
Journal of Guidance, Control, and Dynamics, 1 November 2001, vol.
24, no. 6, pp. 1214-1222(9), Ingenta.
- Computing the zeros of quaternion polynomials
Serodio R.; Pereira E.; Vitoria J.
Computers and Mathematics with Applications, October 2001, vol.
42, no. 8, pp. 1229-1237(9), Ingenta.
- Consimilarity of quaternion matrices and complex matrices
Liping H.
Linear Algebra and its Applications, 1 July 2001, vol. 331, no. 1,
pp. 21-30(10), Ingenta.
- Angular-Rate Estimation Using Delayed Quaternion
Measurements
Azor R.; Bar-Itzhack I. Y.; Deutschmann J. K.; Harman R. R.
Journal of Guidance, Control, and Dynamics, 1 May 2001, vol. 24,
no. 3, pp. 436-443(8)), Ingenta.
- Zeros of Quaternion Polynomials
Serodio R.; Siu L.-S.
Applied Mathematics Letters, February 2001, vol. 14, no. 2, pp.
237-239(3)), Ingenta.
- New Method for Extracting the Quaternion from a Rotation
Matrix
Bar-Itzhack I. Y.
Journal of Guidance, Control, and Dynamics, 1 November 2000, vol.
23, no. 6, pp. 1085-1087(3)), Ingenta.
- Unit quaternion integral curve: A new type of fair free-form
curves
Miura K.T.
Computer Aided Geometric Design, January 1999, vol. 17, no. 1, pp.
39-58(20)), Ingenta.
- Generalisation of the Mandelbrot set to integral functions of
quaternions.
Gomatam, Jagannathan; McFarlane, Isobel
Discrete Contin. Dynam. Systems 5 (1999), no. 1, 107--116,
MathSciNet.
- Stable norms on complex numbers and quaternions.
Arens, Richard; Goldberg, Moshe; Luxemburg, W. A. J.
J. Algebra 219 (1999), no. 1, 1--15, MathSciNet.
- Littlewood's algorithm and quaternion matrices
Merino D.I.; Sergeichuk V.V.
Linear Algebra and its Applications, 1 September 1999, vol. 298,
no. 1, pp. 193-208(16)), Ingenta.
- Quaternion matrix and the Re-nonnegative definite solutions to
the quaternion matrix inverse problem AX=B.
Xiantao, Wang
Math. J. Okayama Univ. 39 (1997), 61--69 (1999),
MathSciNet.
- A Characterization of Quaternion Planes, Revisited
Stroppel M.
Geometriae Dedicata, September 1998, vol. 72, no. 2, pp.
179-187(9)), Ingenta.
- Integration of the equations of a rotational motion of a rigid
body in quaternion algebra. The Euler case
Niwa Y.; Yamamoto T.; Kawakami H.; Kitazawa Y.; Kosenko I.I.
Journal of Applied Mathematics and Mechanics, 1998, vol. 62, no.
2, pp. 193-200(8), Ingenta.
- Quaternions and Cayley numbers. Algebra and applications.
Ward, J. P.
Mathematics and its Applications, 403. Kluwer Academic Publishers
Group, Dordrecht, 1997. xii+237 pp. ISBN: 0-7923-4513-4,
MathSciNet.
- Quaternions and matrices of quaternions.
Zhang, Fuzhen
Linear Algebra Appl. 251 (1997), 21--57,
MathSciNet.
- Iteration
of Quaternion Functions
Stephen Bedding; Keith Briggs
American Mathematical Monthly, Vol. 103, No. 8. (Oct., 1996), pp.
654-664, Jstor.
- A quaternion solution to the pose determination problem for
rendezvous and docking simulations
Mukundan R.; Ramakrishnan K.R.
Mathematics and Computers in Simulation, 8 November 1995, vol. 39,
no. 1, pp. 143-153(11), Ingenta.
- Singular invariant hyperfunctions on the spaces of symmetric
matrices, and, of complex and quaternion Hermitian matrices.
Muro, Masakazu
Representation theory of groups and analysis on homogeneous spaces
(Japanese) (Kyoto, 1995). Surikaisekikenkyusho Kokyuroku No. 929
(1995), 19--40, MathSciNet.
- Explanation in the historiography of mathematics: the case of
Hamilton's quaternions.
Koetsier, Teun
Stud. Hist. Philos. Sci. 26 (1995), no. 4, 593--616,
MathSciNet.
- On numerical range of normal matrices of quaternions.
Zhang, Fuzhen
J. Math. Phys. Sci. 29 (1995), no. 6, 235--251,
MathSciNet.
- Interpolating solid orientations with circular blending
quaternion curves
Kim M.-S.; Nam K.-W.
Computer-Aided Design, May 1995, vol. 27, no. 5, pp. 385-398(14),
Ingenta.
- Fractals, chaos and quaternions.
Doyle, John F.; Steves, Bonnie; Gomatam, Jagannathan
From Newton to chaos (Cortina d'Ampezzo, 1993), 417--422, NATO
Adv. Sci. Inst. Ser. B Phys., 336, Plenum, New York, 1995,
MathSciNet.
- The numerical range of normal matrices with quaternion
entries.
So, Wasin; Thompson, Robert C.; Zhang, Fu Zhen
Special Issue: The numerical range and numerical radius. Linear
and Multilinear Algebra 37 (1994), no. 1-3, 175--195,
MathSciNet.
- Generalization of the de Moîvre formulas for quaternions
and octonions.
Leite, F. Silva; Vitória, José
Mathematical studies in honor of Professor Luís de
Albuquerque (Portuguese), 121--133, Univ. Coimbra, Coimbra, 1994,
MathSciNet.
- Division algebras: octonions, quaternions, complex numbers and
the algebraic design of physics.
Dixon, Geoffrey M.
Mathematics and its Applications, 290. Kluwer Academic Publishers
Group, Dordrecht, 1994. x+236 pp. ISBN: 0-7923-2890-6,
MathSciNet.
- Quaternions and the heuristic role of mathematical structures
in physics.
Anderson, Ronald; Joshi, Girish C.
Phys. Essays 6 (1993), no. 2, 308--319,
MathSciNet.
- The quaternion formalism for Möbius groups in four or
fewer dimensions.
Wilker, J. B.
Linear Algebra Appl. 190 (1993), 99--136, MathSciNet
- Quaternion solutions of four-dimensional Liouville and
sine-Gordon equations.
Chung, Won-Sang; Lee, Jungjai; Cho, Jin-Ho
Modern Phys. Lett. A 7 (1992), no. 27, 2527--2533,
MathSciNet.
- A quaternion representation of the Lorentz group for classical
physical applications
Abonyi I.; Bito J.F.; Tar J.K.
Journal of Physics A: Mathematical and General, 1991, vol. 24, no.
14, pp. 3245-3254(10), Ingenta.
- Application of the quaternion method to a generalization of
the Kolosov-Muskhelishvili method to three-dimensional problems of
elasticity theory. (Russian)
Pimenov, A. A.; Pushkarev, V. I.
Prikl. Mat. Mekh. 55 (1991), no. 3, 422--427; translation in J.
Appl. Math. Mech. 55 (1991), no. 3, 343--347 (1992),
MathSciNet.
- Arithmetic of quaternions and Eisenstein series. (Russian)
Gritsenko, V. A.
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 160
(1987), Anal. Teor. Chisel i Teor. Funktsii. 8, 82--90, 298;
translation in J. Soviet Math. 52 (1990), no. 3, 3056--3063,
MathSciNet.
- The origin of quaternions. (Spanish)
Rosales Góngora, Antono
Epsilon No. 13 (1989), 43--50, MathSciNet.
- Hamilton,
Rodrigues, and the Quaternion Scandal
Simon L. Altmann
Mathematics Magazine, Vol. 62, No. 5. (Dec., 1989), pp. 291-308,
Jstor.
- A Quick Introduction to
Quaternions
McAllister, Byron L.
Pi Mu Epsilon J., (1989), V. 9, No. 1, pp. 23-25.
- Classes of quaternion algebras in the Brauer group. Quadratic
forms and real algebraic geometry (Corvallis, OR, 1986).
Miná\v c, Ján
Rocky Mountain J. Math. 19 (1989), no. 3, 819--831,
MathSciNet.
- Doubling:
Real, Complex, Quaternion, and beyond... Well, Maybe (in Classroom
Capsules)
Robert C. Moore
The College Mathematics Journal, Vol. 17, No. 4. (Sep., 1986), pp.
342-343, Jstor.
- Some norm conditions for a Banach algebra to be either the
reals, complexes or quaternions.
Okada, Nolio
TRU Math. 19 (1983), no. 1, 67--74, MathSciNet.
- Vector
Identities from Quaternions (in Classroom
Capsules)
William C. Schulz
The Two-Year College Mathematics Journal, Vol. 12, No. 4. (Sep.,
1981), pp. 271-273, Jstor.
- Equivalence
of an Identity in Vector Analysis to Quaternion Associativity, and
Ramifications (in Classroom Notes)
Andrew Sobczyk
American Mathematical Monthly, Vol. 88, No. 6. (Jun. - Jul.,
1981), pp. 441-443, Jstor.
- A
Rational Polynomial whose Group is the Quaternions (in
Mathematical Notes)
Richard A. Dean
American Mathematical Monthly, Vol. 88, No. 1. (Jan., 1981), pp.
42-45, Jstor.
- Solution of the Dirac equation in quaternions. (Russian)
Berezin, A. V.; Tolkachev, E. A.; Fedorov, F. I.
Izv. Vyssh. Uchebn. Zaved. Fiz. 1981, no. 10, 43--46,
MathSciNet.
- Extension and reduction of the range in modular quaternion
arithmetic. (Russian)
Turmuhambetov, R. N.
Theory of coding and complexity of calculations (Russian), pp.
195--207, 224, "Nauka" Kazakh. SSR, Alma-Ata, 1980,
MathSciNet.
- The Lorentz transformations and the equations for spinorial
quaternions. (Russian)
Berezin, A. V.; Tolkacev, E. A.; Fedorov, F. I.
Dokl. Akad. Nauk BSSR 24 (1980), no. 4, 308--310, 380,
MathSciNet.
- Quaternion factorization of the Klein-Fok operator.
(Russian)
Ermolaev, E. A.
Vestsi Akad. Navuk BSSR Ser. Fi z.-Mat. Navuk 1979, no. 1, 75--78,
141, MathSciNet.
- Quaternion quantum mechanics as the description of tachyons
and quarks.
Soucek, J.
Symposium on Mathematical Models in the Theory of Elementary
Particles (Liblice, 1978), II. Czechoslovak J. Phys. B 29 (1979),
no. 3, 315--318, MathSciNet.
- Pseudo-quaternion and pseudo-octonion algebras.
Okubo, Susumu
Hadronic J. 1 (1978), no. 4, 1250--1278,
MathSciNet.
- Real subspaces of a quaternion vector space.
Dlab, Vlastimil; Ringel, Claus Michael
Canad. J. Math. 30 (1978), no. 6, 1228--1242,
MathSciNet.
- Complex quaternions and spinor representations of de Sitter
groups SO(4,1) and SO(3,2).
Mir-Kasimov, R. M.; Volobujev, I. P.
Acta Phys. Polon. B 9 (1978), no. 2, 91--105,
MathSciNet.
- Special methods of prescribing a complete residue system in
the ring of quaternions. (Russian)
Turmuhambetov, R. N.
Theoretical and applied problems in mathematics and mechanics
(Russian), pp. 290--291, 317, "Nauka" Kazakh. SSR, Alma-Ata, 1977,
MathSciNet.
- Hamilton's
Discovery of Quaternions
B. L. van der Waerden
Mathematics Magazine, Vol. 49, No. 5. (Nov., 1976), pp. 227-234,
Jstor.
- Existence of a quaternion matrix with prescribed eigenvalues
and diagonal elements of special form. (Russian)
Bredihin, B. S.
Izv. Voronezh. Gos. Ped. Inst. 189 (1976), 50--51,
MathSciNet.
- Hamilton's discovery of quaternions.
van der Waerden, B. L.
Translated from the German by F. V. Pohle. Math. Mag. 49 (1976),
no. 5, 227--234, MathSciNet.
- Are quaternions any use?
Abrahamson, B.
Math. Colloq. Univ. Cape Town 10 (1975/76), 114--127,
MathSciNet.
- Second quantized quaternion quantum theory.
Edmonds, James D., Jr.
Found. Phys. 5 (1975), no. 4, 643--648,
MathSciNet.
- A model of hyperbolic stereometry based on the algebra of
quaternions.
Szybiak, A.
Colloq. Math. 32 (1975), no. 2, 277--284,
MathSciNet.
- On Analytic Function of a Quaternion
Variable
Buoncristiana, A. M.
Pi Mu Epsilon J., (1974), V. 6, No. 1, pp. 8-11.
- The
Quaternion Calculus
C. A. Deavours
American Mathematical Monthly, Vol. 80, No. 9. (Nov., 1973), pp.
995-1008, Jstor.
- Numerical calculation of quaternion functions. IV.
Hoshi, Seiichi
Mem. Fac. Engrg. Miyazaki Univ. No. 7 (1973), 1--34,
MathSciNet.
- A classification of the lines n-dimensional real-complex
affine space over the sfield of quaternions. (Russian)
Moscennikova, G. A.
Questions of differential and non-Euclidean geometry (Russian),
pp. 146--168. Moskov. Gos. Ped. Inst., Moscow, 1972 (1973),
MathSciNet.
- On the definitions of complex numbers and quaternions.
Ravaska, Timo
Nordisk Mat. Tidskr. 19 (1971), 134--136, 155,
MathSciNet.
- Reducible locally nilpotent matrix groups over sfield of real
quaternions. (Russian)
Zagorin, L. E.
Vesci Akad. Navuk BSSR Ser. Fi z.-Mat. Navuk 1969 no. 2, 115--117,
MathSciNet.
- The
Quaternion Group in Plane Geometry
K. Sitaram
Proceedings of the American Mathematical Society, Vol. 19, No. 4.
(Aug., 1968), pp. 857-858, Jstor.
- The
Involutory Antiautomorphisms of the Quaternion Algebra (in
Mathematical Notes)
Rabe Von Randow
American Mathematical Monthly, Vol. 74, No. 6. (Jun. - Jul.,
1967), pp. 699-700, Jstor.
- From the universal arithmetic of Newton to the quaternion
algebra of Hamilton. (Russian)
Kramar, F. D.
Istor.-Mat. Issled. No. 17 1966 309--316,
MathSciNet.
- Semi-quaternion symplectic straight line. (Russian)
Luscickaja, I. G.; Sestyreva, L. V.
Taskent. Gos. Univ. Nau\v cn. Trudy Vyp. 276 1966 62--70,
MathSciNet.
- An integral theorem for analytic intrinsic functions on
quaternions.
Cullen, C. G.
Duke Math. J. 32 1965 139--148, MathSciNet.
- Another proof of the theorems on the eigenvalues of a square
quaternion matrix.
Au-yeung, Yik-hoi
Proc. Glasgow Math. Assoc. 6 1964 191--195 (1964),
MathSciNet.
- The
Geometric Theory of Quaternions
W. F. Eberlein
American Mathematical Monthly, Vol. 70, No. 9. (Nov., 1963), pp.
952-954, Jstor.
- Complex
Fibonacci Numbers and Fibonacci Quaternions (in Mathematical
Notes)
A. F. Horadam
American Mathematical Monthly, Vol. 70, No. 3. (Mar., 1963), pp.
289-291, Jstor.
- Analytic primary functions on quaternions.
Cullen, C. G.
Mem. School Sci. Engrg. Waseda Univ. Tokyo No. 27 1963 103--106,
MathSciNet.
- Foundations of quaternion quantum mechanics.
Finkelstein, David; Jauch, Josef M.; Schiminovich, Samuel;
Speiser, David
J. Mathematical Phys. 3 1962 207--220,
MathSciNet.
- Some theorems on matrices with real quaternion elements.
Wiegmann, N. A.
Canad. J. Math. 7, (1955). 191--201, MathSciNet.
- A
Matric Proof of the Fundamental Theorem of Algebra for Real
Quaternions (in Mathematical Notes)
Mark Leum; M. F. Smiley
American Mathematical Monthly, Vol. 60, No. 2. (Feb., 1953), pp.
99-100, Jstor.
- Quaternions
and Hadamard Matrices
W. A. Rutledge
Proceedings of the American Mathematical Society, Vol. 3, No. 4.
(Aug., 1952), pp. 625-630, Jstor.
- An
Elementary Note on Powers of
Quaternions
H. E. Salzer
American Mathematical Monthly, Vol. 59, No. 5. (May, 1952), pp.
298-300, Jstor.
- An elementary note on powers of quaternions.
Salzer, H. E.
Amer. Math. Monthly 59, (1952). 298--300,
MathSciNet.
- The
Use of Quaternions in Wave-Tensor
Calculus
C. W. Kilmister
Proceedings of the Royal Society of London. Series A, Mathematical
and Physical Sciences, Vol. 199, No. 1059. (Dec. 7, 1949), pp.
517-532, Jstor.
- Eigenvalues and canonical forms of matrices with quaternion
coefficients.
Lee, H. C.
Proc. Roy. Irish Acad. Sect. A. 52, (1949). 253--260,
MathSciNet.
- Onderzoekingen betreffende de Meetkundige Grondslagen van de
Projectieve Quaternionenmeetkunde. (Dutch)
Bilo, Julien
[Investigations on the Geometrical Foundations of Projective
Quaternion Geometry] A. Vanderlinden, Brussel,] 1949. 123
pp., MathSciNet.
- Stereographic projection and the linear fractional group of
transformations of quaternions.
Gormley, P. G.
Proc. Roy. Irish Acad. Sect. A. 51, (1947). 67--85,
MathSciNet.
- Quaternions
and Reflections (Postscript) (in Discussions and
Notes)
H. S. M. Coxeter
American Mathematical Monthly, Vol. 53, No. 10. (Dec., 1946), p.
588, Jstor.
- Quaternions
and Reflections
H. S. M. Coxeter
American Mathematical Monthly, Vol. 53, No. 3. (Mar., 1946), pp.
136-146, Jstor.
- An elementary presentation of the theory of quaternions.
Murnaghan, F. D.
Scripta Math. 10, (1944). 37--49, MathSciNet.
- The
Roots of a Quaternion
Louis Brand
American Mathematical Monthly, Vol. 49, No. 8. (Oct., 1942), pp.
519-520, Jstor.
- Quaternions
and Sums of Three Squares
Gordon Pall
American Journal of Mathematics, Vol. 64, No. 1/4. (1942), pp.
503-513, Jstor.
- The
Roots of a Quaternion
Ivan Niven
American Mathematical Monthly, Vol. 49, No. 6. (Jun. - Jul.,
1942), pp. 386-388, Jstor.
- The roots of a quaternion.
Brand, Louis
Amer. Math. Monthly 49, (1942), MathSciNet.
- Equations
in Quaternions
Ivan Niven
American Mathematical Monthly, Vol. 48, No. 10. (Dec., 1941), pp.
654-661, Jstor.
- On some applications of quaternions to restricted relativity
and classical radiation theory.
Weiss, P.
Proc. Roy. Irish Acad. Sect. A. 46, (1941). 129--168,
MathSciNet.
- On
the Arithmetic of Quaternions
Gordon Pall
Transactions of the American Mathematical Society, Vol. 47, No. 3.
(May, 1940), pp. 487-500, Jstor.
- Quaternion
Treatment of the Relativistic Wave
Equation
A. W. Conway
Proceedings of the Royal Society of London. Series A, Mathematical
and Physical Sciences, Vol. 162, No. 909. (Sep. 15, 1937), pp.
145-154, Jstor.
- Doubly
Divisible Quaternions
Horace L. Olson
The Annals of Mathematics, 2nd Ser., Vol. 31, No. 3. (Jul., 1930),
pp. 371-374, Jstor.
- Arithmetics
of Generalized Quaternion Algebras
Claiborne G. Latimer
American Journal of Mathematics, Vol. 48, No. 1. (Jan., 1926), pp.
57-66, Jstor.
- Quaternion
Developments with Applications
James Byrnie Shaw
Transactions of the American Mathematical Society, Vol. 13, No. 3.
(Jul., 1912), pp. 279-292, Jstor.
- A
Matrix Defined by the Quaternion Group
L. E. Dickson
American Mathematical Monthly, Vol. 9, No. 11. (Nov., 1902), pp.
243-248, Jstor.
- Errata:
A Matrix Defined by the Quaternion
Group
American Mathematical Monthly, Vol. 9, No. 11. (Nov., 1902), p.
276, Jstor.
- Quaternions
and Projective Geometry
Charles Jasper Joly
Philosophical Transactions of the Royal Society of London. Series
A, Containing Papers of a Mathematical or Physical Character, Vol.
201. (1903), pp. 223-327, Jstor.
- Quaternion
Space
Arthur S. Hathaway
Transactions of the American Mathematical Society, Vol. 3, No. 1.
(Jan., 1902), pp. 46-59, Jstor.
- The
Linear Vector Operator of Quaternions
James Byrnie Shaw
American Journal of Mathematics, Vol. 19, No. 3. (Jul., 1897), pp.
267-282, Jstor.
- Application
of Quaternions to Projective Geometry
C. H. Chapman
American Journal of Mathematics, Vol. 14, No. 2. (Apr., 1892), pp.
115-140, Jstor.
- Plane
Trigonometry by Quaternions
De Volson Wood
The Analyst, Vol. 9, No. 1. (Jan., 1882), pp. 19-21,
Jstor.
- The
Quaternion Formulae for Quantification of Curves, Surfaces and
Solids, and for Barycentres
W. I. Stringham
American Journal of Mathematics, Vol. 2, No. 3. (Sep., 1879), pp.
205-210, Jstor.
- Mechanics
by Quaternions
E. W. Hyde
The Analyst, Vol. 8, No. 2. (Mar., 1881), pp. 49-55,
Jstor.
- Mechanics
by Quaternions
E. W. Hyde
The Analyst, Vol. 7, No. 5. (Sep., 1880), pp. 137-144,
Jstor.
- Quaternions
De Volson Wood
The Analyst, Vol. 7, No. 1. (Jan., 1880), pp. 11-13,
Jstor.
- Origin
of the Name "Quaternions"
W. W. Johnson
The Analyst, Vol. 7, No. 2. (Mar., 1880), p. 52,
Jstor.
- A
Certain Class of Cubic Surfaces Treated by
Quaternions
A. B. Chace
American Journal of Mathematics, Vol. 2, No. 4. (Dec., 1879), pp.
315-323, Jstor.
- Quaternions
Christine Ladd
The Analyst, Vol. 4, No. 6. (Nov., 1877), pp. 172-174,
Jstor.
Return
to the Complex Analysis Project
(c) John
H. Mathews 2003