- #1
MathematicalPhysicist
Gold Member
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prove that a 2x2 complex matrix :
a b
c d
is positive iff A=A*, where A* is the conjugate transpose.
i know that an operator (and so i think it also applies to a matrix) is positive when it equals SS* for an operator (matrix) S.
and A* equals:
\\_
a c
_
b d
where the upper line stands for the conjugate.
but i don't know how to find an operator (matrix) which multiplied by its transpose conjugate equals A.
any pointers will be appreciated.
a b
c d
is positive iff A=A*, where A* is the conjugate transpose.
i know that an operator (and so i think it also applies to a matrix) is positive when it equals SS* for an operator (matrix) S.
and A* equals:
\\_
a c
_
b d
where the upper line stands for the conjugate.
but i don't know how to find an operator (matrix) which multiplied by its transpose conjugate equals A.
any pointers will be appreciated.
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