In mathematics, quaternionic analysis is the study of functions with quaternions as the domain and/or range. Such functions can be called functions of...

quaternion (in this case, the sub-field of hypercomplex analysis is called quaternionic analysis). A second instance involves functions of a motor variable...

understand and to work than the Cartesian analysis. But that was before I had thrown off the quaternionic old-man-of-the-sea who fastened himself about...

matrices. The transform is a homography used in real analysis, complex analysis, and quaternionic analysis. In the theory of Hilbert spaces, the Cayley transform...

spin manifold. In 3 and 4 dimensions Clifford analysis is sometimes referred to as quaternionic analysis. When n = 4, the Dirac operator is sometimes referred...

geometry used to describe the physical phenomena of quantum physics Quaternionic analysis Ramsey theory the study of the conditions in which order must appear...

vector analysis, developed out of quaternionic analysis in the late 19th century by Gibbs and Heaviside. The legacy of quaternionic analysis in vector...

Generalization of a derivative of a function between two Banach spaces Quaternionic analysis – Function theory with quaternion variable Semi-differentiability –...

corresponds to the integral, whence the term differintegral. In quaternionic analysis, derivatives can be defined in a similar way to real and complex...

The Lie algebra of Sp(n) is given by the quaternionic skew-Hermitian matrices, the set of n-by-n quaternionic matrices that satisfy A + A † = 0 {\displaystyle...

180, ISBN 978-0-521-37165-0 Kravchenko, Vladislav (2003), Applied Quaternionic Analysis, Heldermann Verlag, ISBN 3-88538-228-8 Lanczos, Cornelius (1949)...

research on algebraic number theory and quaternion analysis proposing a definition of ‘regular’ for quaternionic functions similar to the definition of holomorphic...

and quantum physics). In 1998 he was an Invited Speaker with talk Quaternionic analysis of Riemann surfaces and differential geometry at the International...

specialising in differential geometry and known for her work on quaternionic analysis and Willmore surfaces. She works in England as a reader in mathematics...

orthonormal k-frames in C n {\displaystyle \mathbb {C} ^{n}} and the quaternionic Stiefel manifold V k ( H n ) {\displaystyle V_{k}(\mathbb {H} ^{n})}...

of Quaternionic Hyperfunctions, was supervised by Daniele C. Struppa. Sabadini is the author of multiple books in mathematics including: Analysis of Dirac...

PMLR: 325–343. Imaeda, K.; Imaeda, M. (2000). "Sedenions: algebra and analysis". Applied Mathematics and Computation. 115 (2): 77–88. doi:10.1016/S0096-3003(99)00140-X...

of K contains an Sp(1) summand acting like the unit quaternions on a quaternionic vector space. Thus the quaternion-Kähler symmetric spaces are easily...

other physicists of the convenience of the vectorial approach over the quaternionic calculus of William Rowan Hamilton, which was then widely used by British...

sometimes denoted H(A,σ). 1. The set of self-adjoint real, complex, or quaternionic matrices with multiplication ( x y + y x ) / 2 {\displaystyle (xy+yx)/2}...

the action of an even-graded element on a spinor is given by ordinary quaternionic multiplication. Note that the expression (1) for a vector rotation through...

Following a substantial debate, the mainstream shifted from Hamilton's quaternionic system to Gibbs' three-vectors system. This transition led to the prevalent...

≥ 2. For n ≥ 2, the noncompact Lie group Sp(n, 1) of isometries of a quaternionic hermitian form of signature (n,1) is a simple Lie group of real rank...

a type 2-3-3 triangle J2 is the group of automorphisms preserving a quaternionic structure (modulo its center). Consists of subgroups which are closely...

Eilenberg–Niven theorem, a generalization of the theorem to polynomials with quaternionic coefficients and variables Hilbert's Nullstellensatz, a generalization...

certain spin representations of SO(3), with respect to the action by quaternionic multiplication. Spherical harmonics can be separated into two set of...

U(N) to U(N – 1) states that Example. The unitary symplectic group or quaternionic unitary group, denoted Sp(N) or U(N, H), is the group of all transformations...

representation Semisimple Complex representation Real representation Quaternionic representation Pseudo-real representation Symplectic representation Schur's...

{1}{Z_{{\text{GSE}}(n)}}}e^{-n\mathrm {tr} H^{2}}} on the space of n × n Hermitian quaternionic matrices, e.g. symmetric square matrices composed of quaternions, H =...

mathematics, a hypertoric variety or toric hyperkähler variety is a quaternionic analog of a toric variety constructed by applying the hyper-Kähler quotient...