# Hermitian Matrix

1. May 22, 2014

### S_David

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

2. May 22, 2014

### micromass

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

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

or something similar?

3. May 22, 2014

### S_David

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

4. May 22, 2014

### micromass

Staff Emeritus
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.

5. May 22, 2014

### S_David

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

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