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Numerical radius and zero pattern of matrices |
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| Authors: | Vladimir Nikiforov |
| Institution: | Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA |
| Abstract: | Let A be an n×n complex matrix and r be the maximum size of its principal submatrices with no off-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting ‖A‖ be the Frobenius norm of A, we show that |〈Ax,x〉|2?(1−1/2r−1/2n)‖A‖2. |
| Keywords: | Numerical radius Turá n's theorem Zero pattern _method=retrieve& _eid=1-s2 0-S0022247X07004969& _mathId=si6 gif& _pii=S0022247X07004969& _issn=0022247X& _acct=C000069490& _version=1& _userid=6211566& md5=aa6a2c2aa25b05b1226bc5a998e690b2')" style="cursor:pointer (0" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">(0 1)-Matrices Motzkin-Straus's inequality |
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