We consider two types of spiked multivariate F distributions: a scaled distribution with the scale matrix equal to a rank-k perturbation of the identity, and a distribution with trivial scale, but rank-k non-centrality. The eigenvalues of the rank-r matrix (spikes) parameterize the joint distribution of the eigenvalues of the corresponding F matrix. We show that, for the spikes located above a ...

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed Subspace-Orbit Randomized singular value decomposition (SORSVD), which makes use of random sampling techniques to give an approximation to a low-rank matrix....

results the results of this study showed high reliability and validity of smartphone in regarding ug with icc > 0.95. the highest reliability for both methods was in elbow supination and the lowest was in the elbow flexion (0.84). objectives the study was designed to compare the smartphone inclinometer-based app and ug in evaluation of rom of elbow. materials and methods the maximum rom of elbo...

In this study‎, ‎a new polynomial rank transmutation is proposed with the help of‎ ‎ the idea of quadratic rank transmutation mapping (QRTM)‎. ‎This polynomial rank‎ ‎ transmutation is allowed to extend the range of the transmutation parameter from‎ ‎  [-1,1] to [-1,k]‎‎. ‎At this point‎, ‎the generated distributions gain more&lrm...

Abstract. Any given nonnegative matrix A ∈ R can be expressed as the product A = UV for some nonnegative matrices U ∈ R and V ∈ R with k ≤ min{m, n}. The smallest k that makes this factorization possible is called the nonnegative rank of A. Computing the exact nonnegative rank and the corresponding factorization are known to be NP-hard. Even if the nonnegative rank is known a priori, no simple ...

Suppose that c is a linear operator acting on an n-dimensional complex Hilbert Space H, and let τ denote the normalized trace on B(H). Set b1 = (c + c )/2 and b2 = (c − c)/2i, and write B for the the spectral scale of {b1, b2} with respect to τ . We show that B contains full information about Wk(c), the k-numerical range of c for each k = 1, . . . , n. We then use our previous work on spectral ...

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given m × n matrix A by a matrix B of rank at most k which is much smaller than m and n. The best rank k approximation can be determined via the singular value decomposition which, however, has prohibitively high computational complexity and storage requirements for very large m and...