with science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300076&_mathId=si11.gif&_user=111111111&_pii=S0024379516300076&_rdoc=1&_issn=00243795&md5=1e229d0f94852204a933e39eec5bc835" title="Click to view the MathML source">w(A′)≤|a|/2 and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300076&_mathId=si12.gif&_user=111111111&_pii=S0024379516300076&_rdoc=1&_issn=00243795&md5=164ad8b64e6d682a98ac701b0d6e19d5" title="Click to view the MathML source">w(B′)≤|b|/2. An analogous characterization for the extremal equality for tensor products is also proven. For doubly commuting matrices, we use their unitary similarity model to obtain the corresponding result. For commuting 2-by-2 matrices A and B , we show that science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300076&_mathId=si13.gif&_user=111111111&_pii=S0024379516300076&_rdoc=1&_issn=00243795&md5=f97c4b18274f69cb2bc0035322ca86a1" title="Click to view the MathML source">w(AB)=w(A)w(B) if and only if either A or B is a scalar matrix, or A and B are simultaneously unitarily similar to science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300076&_mathId=si14.gif&_user=111111111&_pii=S0024379516300076&_rdoc=1&_issn=00243795&md5=14ace1731c9857477311226c5cbe8450"> and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300076&_mathId=si15.gif&_user=111111111&_pii=S0024379516300076&_rdoc=1&_issn=00243795&md5=27e83bfbf0dc5c7b801a2b4d06375b28"> with science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300076&_mathId=si16.gif&_user=111111111&_pii=S0024379516300076&_rdoc=1&_issn=00243795&md5=c2023d12b941a19a61824e6063cc325f" title="Click to view the MathML source">|a1|≥|a2| and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300076&_mathId=si17.gif&_user=111111111&_pii=S0024379516300076&_rdoc=1&_issn=00243795&md5=e89e65508fd5889c24ebe41a8ad6aab3" title="Click to view the MathML source">|b1|≥|b2|.