Recognizable classification of Lorentzian distance-squared mappings
نویسندگان
چکیده
منابع مشابه
On Certain Linear Mappings Between Inner-Product and Squared-Distance Matrices
We obtain the spectral decomposition of four linear mappings. The first, Ie, is a mapping of the linear hull of all centered inner-product matrices onto the linear hull of all the induced squared-distance matrices. It is based on the natural generalization of the cosine law of elementary Euclidean geometry. The other three mappings studied are ,,1, the adjoint ,,*, and (" *)1. Extensions and ap...
متن کاملA Lorentzian Gromov-Hausdorff notion of distance
This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...
متن کاملThe limits of squared Euclidean distance regularization
Some of the simplest loss functions considered in Machine Learning are the square loss, the logistic loss and the hinge loss. The most common family of algorithms, including Gradient Descent (GD) with and without Weight Decay, always predict with a linear combination of the past instances. We give a random construction for sets of examples where the target linear weight vector is trivial to lea...
متن کاملOn Classification of Lorentzian Kac–moody Algebras
We discuss a general theory of Lorentzian Kac–Moody algebras which should be a hyperbolic analogy of the classical theories of finite-dimensional semisimple and affine Kac–Moody algebras. First examples of Lorentzian Kac–Moody algebras were found by Borcherds. We consider general finiteness results about the set of Lorentzian Kac–Moody algebras and the problem of their classification. As an exa...
متن کاملTowards a classification of Lorentzian holonomy groups
If the holonomy representation of an (n + 2)–dimensional simply-connected Lorentzian manifold (M,h) admits a degenerate invariant subspace its holonomy group is contained in the parabolic group (R×SO(n))⋉R. The main ingredient of such a holonomy group is the SO(n)–projection G := prSO(n)(Holp(M,h)) and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2014
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2014.03.005