Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416419 | Linear Algebra and its Applications | 2014 | 14 Pages |
Abstract
For an m-order n-dimensional Hilbert tensor (hypermatrix) Hn=(Hi1i2â¯im),Hi1i2â¯im=1i1+i2+â¯+imâm+1,i1,â¦,im=1,2,â¦,n its spectral radius is not larger than nmâ1sinÏn, and an upper bound of its E-spectral radius is nm2sinÏn. Moreover, its spectral radius is strictly increasing and its E-spectral radius is nondecreasing with respect to the dimension n. When the order is even, both infinite and finite dimensional Hilbert tensors are positive definite. We also show that the m-order infinite dimensional Hilbert tensor (hypermatrix) Hâ=(Hi1i2â¯im) defines a bounded and positively (mâ1)-homogeneous operator from l1 into lp (1
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yisheng Song, Liqun Qi,