document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40403>Question 40403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Proof of Hermitian matrices: If A and B are Hermitian matrices, I need to show that BA = AB iff AB is Hermitian, but I can't figure out how...   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26156 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A AND B ARE COMPLEX HERMITIAN MATRICES OF ORDER (N,N)						<BR>\n" );
document.write( "LET TRANSPOSE OF A AND B BE A' AND B'						<BR>\n" );
document.write( "SINCE A,B ARE HERMITIAN,WE HAVE 						<BR>\n" );
document.write( "A=CONJUGATE (A') AND B= CONJ(B')……………………….I						<BR>\n" );
document.write( "CASE 1.						<BR>\n" );
document.write( "AB IS HERMITIAN.LET AB=C…..SO AB=C=CONJ(C')=CONJ(AB)'…………..II						<BR>\n" );
document.write( "C'=(AB)'=B'A'						<BR>\n" );
document.write( "CONJ(C')=CONJ(B'A')=CONJ(B')CONJ(A')=BA…FROM I						<BR>\n" );
document.write( "BUT AB=CONJ(C') FROM II						<BR>\n" );
document.write( "SO AB=BA						<BR>\n" );
document.write( "CASE 2.						<BR>\n" );
document.write( "AB=BA= CONJ(B')CONJ(A')=CONJ(B'A')=CONJ(AB)'=AB…..						<BR>\n" );
document.write( "HENCE AB IS HERMITIAN. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );