Question

if A and B hermitian (skew hermitian) then A+B is also hermitian (skew hermitian) prove the theorem​

Answer 1

Both A and B are also Hermitian. SIMPLY INTERESTING.

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Answer 2

Answer:

If A and B are hermitian matrices or, skew hermitian matrix, so is also A + B

Step-by-step explanation:

• A and B are hermitian. So, $A^{H} = A , B^{H}= B$ (where $A^{H}$ and $B^{H}$ is the transpose conjugate of A and B)

• So, $(A+B)^{H} = A^{H} +B^{H} = (A+B)$ (as,$A^{H} = A , B^{H}= B$ )

• A+B is hermitian matrix.
• A and B are skew hermitian. So,  $A^{H} = -A , B^{H}= -B$ (where $A^{H}$ and $B^{H}$ is the transpose conjugate of A and B)

• So, $(A+B)^{H} = -A^{H} -B^{H} = -A-B=-(A+B)$ (as,$A^{H} = -A , B^{H}= -B$ )
• A+B is skew hermitian matrix.

To learn more about hermitian:

https://brainly.in/question/996920

To learn more about skew hermitian:

https://brainly.in/question/12216099

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