The matrix `[{:(" "0,-4+i),(4+I," "0):}]` is

Options

A. symmetric
B. skew-symmetric
C. Hermitian
D. skew-Hermitian

Answer

D

Explanation

The given matrix `A=[(0,-4+i),(4+i,0)]`
Now, from option:
From option (a): For Symmetric matrix
`A^(T)=A`
Now, `A^(T)=[(0,4+i),(-4+i,0)]ne A`
`therefore" ""The given matrix is not symmetric"`
`therefore" ""option (a) is wrong."`
From option (b): for Skew-symmetric matrix
`A^(T)=-A`
`=[(0,4+i),(-4+i,0)]ne-A`
`therefore" ""given matrix is not skew-symmetric"`
`therefore" ""option (b) is wrong."`
From option(c): For Hermitian matrix
`A^(T)=bar(A)", where "bar(A)` is conjugate of matrix A
`bar(A)=[(0,-4-i),(4-i,0)]neA^(T)`
`therefore" ""option(c) is wrong."`
From option (d): for Skew-Hermitian matrix
The diagonal element of a skew-hermitian matrix are pure imaginary or zero.
`A=[(0,-4+i),(4+i,0)]`
Here, diagonal element indicates that the given matrix is skew-hermitian matrix.
`therefore" ""option (d) is correct."`