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Question

Which of the following represents the condition for a matrix A to be hermitian Matrix. Given that the general element of the matrix is aij.


A

aij=¯¯¯¯¯¯¯aij

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B

aij=¯¯¯¯¯¯¯aji

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C

aij=¯¯¯¯¯¯¯aji

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D

¯¯¯¯¯¯¯aij=aij

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Solution

The correct option is B

aij=¯¯¯¯¯¯¯aji


Try to remember the definition of hermitian matrix. A square matrix is hermitian if it ia equal to its conjugate transpose.

We know that if we take an element aij from a square matrix. The corresponding element in its transpose will be aji. If we take both transpose and conjugate the corresponding element becomes ¯¯¯¯¯¯¯aji. So by definition we can say, ¯¯¯¯¯¯¯aji=aij.

Or,

aij=¯¯¯¯¯¯¯aji. Which is the required condition as per the definition


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