MatFromBlocks
Creates a block matrix by specifying its blocks.
Syntax

MatFromBlocks(n, A[, B[, ...]])

n
is a positive integer 
A, B, ...
are matrices

Description
If n
is a positive integer and A, B, ...
a sequence of matrices, then MatFromBlocks(n, A, B, ...)
returns the block matrix consisting of the blocks A, B, ...
in rowmajor with n
block columns.
The matrices must be of compatible sizes. The number of matrices need not be a multiple of n
; the last block row of the result will be filled with zero blocks if trailing blocks are missing. The number of block rows in the result is ⌈#'(A, B, ...)/n⌉
.
Examples
A ≔ ❨❨1, 2❩, ❨3, 4❩❩; B ≔ ❨❨5, 1, 3❩, ❨1, 0, 2❩❩; C ≔ ❨❨5, 1❩, ❨0, 1❩❩; D ≔ ❨❨5, 1, 2❩, ❨5, 6 ,7❩❩;
MatFromBlocks(2, A, B, C, D)
⎛1 2 5 1 3⎞ ⎜3 4 1 0 2⎟ ⎜5 1 5 1 2⎟ ⎝0 1 5 6 7⎠
MatFromBlocks(2, A, B, C)
⎛1 2 5 1 3⎞ ⎜3 4 1 0 2⎟ ⎜5 1 0 0 0⎟ ⎝0 1 0 0 0⎠
MatFromBlocks(2, A, B)
⎛1 2 5 1 3⎞ ⎝3 4 1 0 2⎠
See also

Creating a matrix (conceptual)