Can I Write a Hermitian Matrix as A=A^(1/2)AH^(1/2)?

[EngWiPy]

Hello,

If I have a Hermitian matrix A, can I write it as:

$$\mathbf{A}=\mathbf{A}^{1/2}\mathbf{A}^{H/2}$$

where superscript H denotes hermitian operation?

Thanks

 

[micromass]

What do you mean with $H/2$? Do you mean

$$(A^H)^{1/2}$$

or something similar?

 

[EngWiPy]

What do you mean with $H/2$? Do you mean

$$(A^H)^{1/2}$$

or something similar?

Yes exactly, it means the square root of the complex conjugation transpose of A.

 

[micromass]

OK, but if $A$ is hermitian, then $A^H = A$, no? So you can write your original post as

$$A = A^{1/2}A^{1/2}$$

which is certainly true.

 

[EngWiPy]

OK, but if $A$ is hermitian, then $A^H = A$, no? So you can write your original post as

$$A = A^{1/2}A^{1/2}$$

which is certainly true.

Oh, I didn't see it that way. Thanks