Moment of inertia & Product of inertia:

The angular momentum of $\vec{L}$ of a rigid body in vector notation can be represented as

$\vec{L}=\overleftrightarrow{I}\vec{\omega}$

where, $\overleftrightarrow{I}=\begin{bmatrix}I_{xx}&I_{xy}&I_{xz}\\I_{yx}&I_{yy}&I_{yz}\\I_{zx}&I{zy}&I_{zz}\end{bmatrix}$ is the moment of inertia tensor.

The three diagonal elements of the moment of inertia tensor $I_{xx}$, $I_{yy}$ and $I_{zz}$ are called the moment of inertia of the rigid body about the rigid body about X, Y and Z axes respectively.

On the other hand the six off-diagonal elements $I_{xy}$, $I_{xz}$, $I_{yx}$, $I_{yz}$, $I_{zx}$ and $I_{zy}$ are called the product of inertia of the rigid body. This occurs in the symmetric pairs i.e.,

$I_{xy}=I_{yx}$, $I_{yz}=I_{zy}$ and $I_{xz}=I_{zx}$.