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Show that if A is a complex square matrix and if   x*Ax  is real for all  x in  Cn( n dimension complex tuple ) , then A is Hermitian.

note: x* stands for Hermitian transpose.
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Originally posted by ±ðÅÂÉÏ»ð at 2011-03-31 19:43:43:
Show that if A is a complex square matrix and if   x*Ax  is real for all  x in  Cn( n dimension complex tuple ) , then A is Hermitian.

note: x* stands for Hermitian transpose.



Õâ¸ö½áÂÛºÍÕý¶¨¾ØÕóûÓйØÏµ~~¸´ÊýÓòµÄHermitian ¾ØÕó¶ÔÓ¦µÄÊÇʵÊýÓòÉϵĶԳƾØÕó~~

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soliton;sato-theory;algebre-geometry£»Random-Matrices-Theory; Riemann-Hilbert method
2Â¥2011-03-31 20:12:43
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ÒÀ´ÎÈ¡ x Ϊµ¥Î»ÕóµÄÿһÁУ¬µÃ I* A I = (I* A I)* = I* A* I  => A=A*
4Â¥2011-03-31 22:32:09
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