| 摘要: | 摘要： For -by- and -by- complex matrices and , it is known that the inequality holds, where and denote, respectively, the numerical radius and the operator norm of a matrix. In this paper, we consider when this becomes an equality. We show that (1) if and , then one of the following two conditions holds: (i) has a unitary part, and (ii) is completely nonunitary and the numerical range of is a circular disc centered at the origin, (2) if for some , , then , and, moreover, the equality holds if and only if is unitarily similar to the direct sum of the -by- Jordan block and a matrix with , and (3) if is a nonnegative matrix with its real part (permutationally) irreducible, then , if and only if either or and is permutationally similar to a block-shift matrix with , where and .
出版者： Abingdon: Taylor & Francis
出版日期： 2015-10-03
出處： Linear & multilinear algebra, 2015-10, Vol.63 (10), p.1916-1936
版權： 2013 Taylor & Francis 2013
版權： 2013 Taylor & Francis
識別號： ISSN: 0308-1087
識別號： EISSN: 1563-5139
識別號： DOI: 10.1080/03081087.2013.839669 |
