# 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)
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I think you will need to specify the submatrices first and then build the block matrix. Of course, you might be able to write your own code to do exactly what you are suggesting.

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Thats a very generic description. Is there something specific which helps?

Some basic things about matrices don't seem to work, like, Z = matrix([[1,0],[2,3]]) Z.charpoly(y)

Those commands are working well for me. But, you must begin by declaring y to be a variable using the command var('y').