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Can I use the block_matrix command to create arbitrary sizes of block matrix arrays?

Like say I want to create a $4k \times 4k$ size matrix by putting together certain $4\times 4$ matrices into a $k \times k$ array.

  • Can the "block_matrix" command help me create such a $4k \times 4k$ array of 0s called $A$ ? (such later I can say something like $A[a,b] = X$ where $0 \leq a,b \leq k$ and $X$ is some $4\times 4$ matrix and that will assign the matrix $X$ at the $(a,b)$ array position)