How can i generate hermitian of a matrix in matlab?

is hermitian of a matrix and complex conjugate transpose are same?..

Answer 1

[pankaj singh]

Transpose for real matrices is equivalent to Hermitian (complex conjugate transpose) for complex matrices. Therefore, you can use the same matlab operator to generate the Hermitian for a complex matrix. For example:

x = [1+j; 1-j; 2-j; 1+2j]         % random complex matrix

x =

   1.0000 + 1.0000i
   1.0000 - 1.0000i
   2.0000 - 1.0000i
   1.0000 + 2.0000i

>> x'                           % take it's Hermitian

ans =

   1.0000 - 1.0000i   1.0000 + 1.0000i   2.0000 + 1.0000i   1.0000 - 2.0000i

Answer 2

[Walter Roberson]

Hermitian is a property, not something that can be generated. A hermitian matrix is a matrix which is equal to its complex transpose.

If you have a matrix which "should" be hermitian but might not be due to round-off error, then take

newH = (H + H') / 2

[Midhun]

Thanks for the info..

[David Mis]

For clarification: "A Hermitian" means the conjugate transpose of A, and it is indeed something that can be generated (in MATLAB we use A' as in pankaj singh's answer). This phrasing is distinct from "A is Hermitian", which means A has the property Walter mentions.

[Zaid Ahmad]

Actually theoretically matrix is hermitian if conjugate of A transpose is A itself. So it is a property. But usually the word hermitian is used as short for hermitian transpose.

[Bruno Luong]

I only know Hermitian, or conjugate transpose.

Rarely heard "complex transpose" or "hermitian transpose".