Four deviations suffice for rank 1 matrices
نویسندگان
چکیده
منابع مشابه
Six Standard Deviations Suffice
Given n sets on n elements it is shown that there exists a two-coloring such that all sets have discrepancy at most Kn>/2, K an absolute constant. This improves the basic probabilistic method with which K = c(ln«)1/2. The result is extended to 11 finite sets of arbitrary size. Probabilistic techniques are melded with the pigeonhole principle. An alternate proof of the existence of Rudin-Shapiro...
متن کاملSix Standard Deviations Suffice
With χ : Ω → {−1,+1} random, A ∈ A, χ(A) has zero mean and standard deviation at most √ n. If |χ(A)| > 6√n then χ(A) is at least six standard deviations off the mean. The probability of this occurring is very small but a fixed positive constant and the number of sets A is going to infinity. In fact, a random χ almost always will not work. The specific constant 6 (actually 5.32) was the result o...
متن کاملSome rank equalities for finitely many tripotent matrices
A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations. Moreover, by using this equality and Theorems 8 and 10 in [Chen M. and et al. On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications, The Scientific World Journal 2014 (2014), Article ID 702413, 7 page...
متن کاملOptimal Low-Rank Tensor Recovery from Separable Measurements: Four Contractions Suffice
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us to consider the problem of low rank tensor recovery from a class of linear measurements called separable measurements. As specific examples, we focu...
متن کاملNoncollision Singularities: Do Four Bodies Suffice!
then we say that there is a collision between bodies i and j at t = t∗. Can there be a singularity without a collision? For example, Poincaré suggested, ri(t) might tend to infinity, or oscillate wildly (like sin 1 t ) as t→ t∗. Although Poincaré never wrote anything about noncollision singularities, Painlèvé gave him credit for being the first to ask this question. Painlèvé himself was able to...
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: Advances in Mathematics
سال: 2020
ISSN: 0001-8708
DOI: 10.1016/j.aim.2020.107366