I have a $M \times N$ matrix $\mathbf{A}$, such that $\mathbf{A^HA}$ is a Hermitian matrix and $M < N$. Is there any way by which I can prove mathematically that $\mathbf{A^H A}$ is Hermitian.
Or should $\mathbf{A}$ have some special structure which can be used to show that $\mathbf{A^H}$ is Hermitian.
The matrix in my problem is such that the correlation between the rows decreases with the separation. In other words, the correlation between the rows of the matrix will be a sinc function. Similar property is also observed for the column matrix. In general the $\mathbf{A}$ has the following form,
$$\mathbf{A}= \begin{bmatrix} 1 & e^{j\pi \theta_1} & e^{j \pi 2\theta_1} & \dots & e^{j \pi N \theta_1} \\ 1 & e^{j\pi \theta_2} & e^{j \pi 2\theta_2} & \dots & e^{j \pi N \theta_2} \\ 1 & e^{j\pi \theta_3} & e^{j \pi 2\theta_3} & \dots & e^{j \pi N \theta_3} \\ \end{bmatrix}$$
Using $(UV)^H=V^HU^H$, $(A^HA)^H=A^H(A^H)^H=A^HA$.