منابع مشابه
Introduction to Tensor Calculus for General Relativity
There are three essential ideas underlying general relativity (GR). The first is that spacetime may be described as a curved, four-dimensional mathematical structure called a pseudo-Riemannian manifold. In brief, time and space together comprise a curved fourdimensional non-Euclidean geometry. Consequently, the practitioner of GR must be familiar with the fundamental geometrical properties of c...
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The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of bor...
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The gravitational Higgs mechanism proposed by ’t Hooft in arXiv:0708.3184 involves the spacetime metric gμν as well as the induced metric gμν ∝ ηab∂μφ∂νφ where φa (a = 0, . . . , 3), as we call it, break all four diffeomorphisms spontaneously via the vacuum expectation values 〈φa〉 ∝ xa. In this framework, we construct and analyze the most general action density in terms of various invariants in...
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Previous work has demonstrated that the image variations of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces. The typical linear subspace learning algorithms include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projection (LPP). All of these methods consider an n1 × n2 ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1937
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1937-06562-1