Make isotropic tensor anisotropic and viceversa?

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Let's say I have an isotropic tensor in 3D [the identity matrix] of the form $$I=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$$ I understand that this tensor is invariant to rotations meaning that the standard tensor rotation would leave the initial tensor unchanged:

$$ I=RIR^T$$

My question is, what is the correct way to make this tensor such that it only has components like this: $$I'=\begin{bmatrix}1&0&0\\0&1&0\\0&0&0\end{bmatrix}$$ Or this: $$I'=\begin{bmatrix}0&0&0\\0&0&0\\0&0&1\end{bmatrix}$$

Or an in-between case such as: $$I'=\begin{bmatrix}0.3&0&0\\0&0.3&0\\0&0&0.5\end{bmatrix}$$ [These are just random values]

Any suggestions are greatly appreciated!