SOLUTION: show that every square matrix can be expressed in one way onl as a sum of hermitian and skew hermitian matrix

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Question 985011: show that every square matrix can be expressed in one way onl as a sum of hermitian and skew hermitian matrix
Answer by solver91311(24713) About Me  (Show Source):
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Let be the given square matrix.

Let where is hermitian and is skew hermitian which is to say: and :(1)

Therefore, ( using the property of transpose of a matrix)

or from (1) above.

Since is square and are defined.

Hence

and

Therefore

and

It is left as an exercise for the student to verify that is hermitian and is skew hermitian.

Therefore, can be uniquely expressed as sum of a hermitian matrix and a skew hermitian matrix, which is:



John

My calculator said it, I believe it, that settles it