Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si1.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=68afdbab74ef306fbe5169bdb4ff33b6" title="Click to view the MathML source">n∈Nclass="mathContainer hidden">class="mathCode"> and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si2.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=12fa6b5803cb9c90042dea4dbd230a63" title="Click to view the MathML source">[Ajk]j,k=1,2class="mathContainer hidden">class="mathCode"> be a Hermitian class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si3.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=68d16c7c3b23fe58b8bd465225b2ed3c" title="Click to view the MathML source">2n×2nclass="mathContainer hidden">class="mathCode"> matrix partitioned into four quadratic matrices class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si4.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=593b14198741b273dd50d9afc7512834" title="Click to view the MathML source">Ajkclass="mathContainer hidden">class="mathCode"> of order n . Marcus and Watkins proved in 1971 that class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si5.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=330090572a621aa1e6307d9384747692">class="imgLazyJSB inlineImage" height="21" width="49" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S002437951630204X-si5.gif">class="mathContainer hidden">class="mathCode"> is positive semidefinite whenever class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si13.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=94b3944a325a60b33f1e70298054ed28" title="Click to view the MathML source">[Ajk]class="mathContainer hidden">class="mathCode"> is positive semidefinite. Let A be an class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si7.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=1928b5eecfc4131eae0378fd7ca7d23d" title="Click to view the MathML source">n×nclass="mathContainer hidden">class="mathCode"> matrix. If f is a class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si8.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=f7be242e8afe27fd4d5dc051b70b14f3" title="Click to view the MathML source">Cclass="mathContainer hidden">class="mathCode">-valued function on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si8.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=f7be242e8afe27fd4d5dc051b70b14f3" title="Click to view the MathML source">Cclass="mathContainer hidden">class="mathCode">, denote by class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si9.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=9a50d7ca091e7f5641191ce44abdc60b" title="Click to view the MathML source">f(A)class="mathContainer hidden">class="mathCode"> the value of the primary matrix function associated with f on the matrix A. If F is a symmetric class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si8.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=f7be242e8afe27fd4d5dc051b70b14f3" title="Click to view the MathML source">Cclass="mathContainer hidden">class="mathCode">-valued function on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si10.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=585aaba47536dd5d5ea1ed5959beeb71" title="Click to view the MathML source">Cnclass="mathContainer hidden">class="mathCode">, let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si11.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=627502b9bfa99a3798d7a3578ba11bfb" title="Click to view the MathML source">F(A)class="mathContainer hidden">class="mathCode"> be the value of F on the eigenvalues of A. Generalizing Marcus and Watkins' result we describe those functions f and F , for which class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si12.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=0946dac7115447a80b1b691e61a74fec" title="Click to view the MathML source">[F(f(Ajk))]class="mathContainer hidden">class="mathCode"> is positive semidefinite whenever class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si13.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=94b3944a325a60b33f1e70298054ed28" title="Click to view the MathML source">[Ajk]class="mathContainer hidden">class="mathCode"> is positive semidefinite. We extend an example by Choudhury, which gives a negative result for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630204X&_mathId=si14.gif&_user=111111111&_pii=S002437951630204X&_rdoc=1&_issn=00243795&md5=6a3ffeda890a1cb5712070d1ce215631" title="Click to view the MathML source">3×3class="mathContainer hidden">class="mathCode"> block matrices.