Is there a matrix that shift data along side the main diagonal?

Question

I am an electrical engineer and I am trying to write my optimization problem in a more compact form. During my time solving this optimization problem, I reallize that I need to keep shifting and augmenting my original data matrix $D = \left[ {\begin{array}{*{20}{c}} 1&1&0\\ 0&1&1 \end{array}} \right]$ along side the diagonal of a resulting matrix like this $R = \left[ {\begin{array}{*{20}{c}} 1&1&0&{}&{}&{}\\ 0&1&1&{}&{}&{}\\ {}&{}&{}&1&1&0\\ {}&{}&{}&0&1&1 \end{array}} \right]$ or $R = \left[ {\begin{array}{*{20}{c}} 1&1&0&{}&{}&{}&{}&{}&{}\\ 0&1&1&{}&{}&{}&{}&{}&{}\\ {}&{}&{}&1&1&0&{}&{}&{}\\ {}&{}&{}&0&1&1&{}&{}&{}\\ {}&{}&{}&{}&{}&{}&1&1&0\\ {}&{}&{}&{}&{}&{}&0&1&1 \end{array}} \right]$.

So my question is: is there a matrix $T$ or transformation $T(D)$ that help me achieve my goal ?

I guess it might have something to do with the Kronecker product but cannot get my head around it.

Would you kindly help me with this ?

Thank you for your enthusiasm !

Answer 1

is there a matrix $T$ or transformation $T(D)$ ... might have something to do with the Kronecker product

Using Direct sum: $$R_n=\bigoplus_{i=1}^{n}D$$ $$R_{n+1}=R_n\oplus D$$

Using Kronecker product: $$R_n=I_n\otimes D$$