Erokhin, V.I., Krasnikov, A.S., Khvostov, M.N., Matrix Corrections Minimal with Respect to the Euclidean Norm for Linear Programming Problems, Automation and Remote Con- trol, 73, No. 2, 219-231 (2012).V. I. Erokhin, A. S. Krasnikov, and M. N. Khvostov, “Matrix corrections minimal with re...
The inclusion of common zeros can be problematic when the matrix is sparse, the distance will become too large to identify differences with rare cases. Mercator::binaryDistance(t(x), metric="russellRao") Simple matching distance 1−a∩b+a¯∩b¯nFor binary data:1−n00+...
*URcontains a 2 by 2 unimodular matrix polynomialUinzsuch thata,b.U=a',b'where(a',b')is the last basis accepted by the algorithm of [2]. Examples > withSNAP: > a≔z6−12.4z5+50.18112+62.53z4−163.542z3+232.9776z2−...
Norm[{1, 2}] == 〈{1, 2}, {1, 2}〉 True Any positive-definite symmetric n-by-n matrix A can be used to define an inner product. If A is an identity matrix, the inner product defined by A is the Euclidean inner product. ■ A nonstandard inner product on the coordinate vector...
We study structural properties and the harmonic analysis of discrete subgroups of the Euclidean group. In particular, we 1. obtain an efficient description of their dual space, 2. develop Fourier analysis methods for periodic mappings on them, and 3. prove a Schur-Zassenhaus type splitting result...
Frobeniusnorm.LetS n + denotetheconeofpositivesemidefinitematricesinS n (oftenabbreviatedasX 0forX∈S n + ).Theso-calledhollowsubspaceS n h is definedby S n h :={A∈S n :diag(A)=0}, wherediag(A)isthevectorformedbythediagonalelementsofA.AmatrixDis anEDMifD∈S n h ,andthereexis...
Anew, the idea is that loga- rithms are much simpler to compute for matrices close to the identity, for in- stance with Pad´e approximants. To transform a matrix M so that it is closer to the identity, the ISS algorithm performs recursive computations of square roots. Then the ...
The dissimilarity matrix (also calleddistance matrix) describes pairwise distinction between M objects. It is a square symmetrical MxM matrix with the (ij)th element equal to the value of a chosen measure of distinction between the (i)th and the (j)th object. ...
It is well-known that a and b are linearly dependent if and only if the determinants of all 2×2 minors of the matrix [a0a1⋯amb0b1⋯bm] vanish. This gives 12m(m+1) conditions, that are quadratic in a0,…,am and b0,…,bm. We can, however, substantially reduce this number ...
Euclidean-Norm-Induced Schatten-p Quasi-Norm Regularization for Low-Rank Tensor Completion and Tensor Robust Principal Component Analysis The nuclear norm and Schatten-p quasi-norm are popular rank proxies in low-rank matrix recovery. However, computing the nuclear norm or Schatten-p quasi-norm of ...