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Question
Which of the following represents the condition for a matrix A to be skew hermitian Matrix. Given that the general element of the matrix is aij.
Which of the following represents the condition for a matrix A to be skew hermitian Matrix. Given that the general element of the matrix is aij.
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Solution
The correct option is C aij=−¯¯¯¯¯¯¯aji
Try to remember the definition of skew hermitian matrix. A square matrix is skew hermitian if its conjugate transpose is equal to its negative.
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 of skew symmetric matrix we can say, ¯¯¯¯¯¯¯aji=−aij.
Or,
aij=¯¯¯¯¯¯¯¯¯¯¯−aji. Which is the required condition as per the definition. Hence correct option is (c)
aij=−¯¯¯¯¯¯¯aji
Try to remember the definition of skew hermitian matrix. A square matrix is skew hermitian if its conjugate transpose is equal to its negative.
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 of skew symmetric matrix we can say, ¯¯¯¯¯¯¯aji=−aij.
Or,
aij=¯¯¯¯¯¯¯¯¯¯¯−aji. Which is the required condition as per the definition. Hence correct option is (c)
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