- #1

MathematicalPhysicist

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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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