@incollection{LAM2003429,
    Abstract = {Publisher Summary This chapter discusses the Hamilton's Quaternions. Hamilton's original motivation was to find an algebraic formalism for the points (x1, x2, x3) in 3-space, in generalization of the formalism of the complex numbers C as pairs of real numbers. A matrix model of the quaternion algebra H is discussed. In modern algebra, a division ring is a ring K with identity 1 ≠ 0 in which every nonzero element is an inverse. These rings are the most ``perfect'' algebraic systems: as one can add, subtract, multiply, and divide. Most of the applications of quaternions to physics are applications of biquaternions. Several other important mathematical developments----namely, Cayley Algebra, Frobenius' Theorem, and Vector Analysis are also described. The fundamental theorem of algebra says that C is an algebraically closed field; that is, any non-constant polynomial in C[x] has a zero in C. The main point of passing from R to C is exactly to get an ``algebraic closure'' of the reals. The features of the quaternions are the role they play in the understanding and representation of the rotations of the low-dimensional Euclidean spaces.},
    Author = {Lam, T.Y.},
    Editor = {Hazewinkel, M.},
    File = {Hamilton's Quaternions - Lam.pdf},
    ISSN = {1570-7954},
    Pages = {429-454},
    Publisher = {North-Holland},
    Series = {Handbook of Algebra},
    Title = {Hamilton's quaternions},
    URL = {https://www.sciencedirect.com/science/article/pii/S1570795403800682},
    Volume = {3},
    Year = {2003},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S1570795403800682},
    bdsk-url-2 = {https://doi.org/10.1016/S1570-7954(03)80068-2},
    date-added = {2022-04-29 22:54:27 +0200},
    date-modified = {2022-04-29 22:54:27 +0200},
    file-2 = {Hamilton's Quaternions - Lam.png},
    file-3 = {quat.ps},
    doi = {10.1016/S1570-7954(03)80068-2}
}

@incollection{LAM2003429, Abstract = {Publisher Summary This chapter discusses the Hamilton's Quaternions. Hamilton's original motivation was to find an algebraic formalism for the points (x1, x2, x3) in 3-space, in generalization of the formalism of the complex numbers C as pairs of real numbers. A matrix model of the quaternion algebra H is discussed. In modern algebra, a division ring is a ring K with identity 1 ≠ 0 in which every nonzero element is an inverse. These rings are the most perfect'' algebraic systems: as one can add, subtract, multiply, and divide. Most of the applications of quaternions to physics are applications of biquaternions. Several other important mathematical developments----namely, Cayley Algebra, Frobenius' Theorem, and Vector Analysis are also described. The fundamental theorem of algebra says that C is an algebraically closed field; that is, any non-constant polynomial in C[x] has a zero in C. The main point of passing from R to C is exactly to get analgebraic closure'' of the reals. The features of the quaternions are the role they play in the understanding and representation of the rotations of the low-dimensional Euclidean spaces.}, Author = {Lam, T.Y.}, Editor = {Hazewinkel, M.}, File = {Hamilton's Quaternions - Lam.pdf}, ISSN = {1570-7954}, Pages = {429-454}, Publisher = {North-Holland}, Series = {Handbook of Algebra}, Title = {Hamilton's quaternions}, URL = {https://www.sciencedirect.com/science/article/pii/S1570795403800682}, Volume = {3}, Year = {2003}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S1570795403800682}, bdsk-url-2 = {https://doi.org/10.1016/S1570-7954(03)80068-2}, date-added = {2022-04-29 22:54:27 +0200}, date-modified = {2022-04-29 22:54:27 +0200}, file-2 = {Hamilton's Quaternions - Lam.png}, file-3 = {quat.ps}, doi = {10.1016/S1570-7954(03)80068-2} }