Wolfram Language & System 11.0 (2016)|Legacy Documentation

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creates a single flattened matrix from a matrix of matrices mi j.

flattens out r pairs of levels in the array a.


  • ArrayFlatten requires that the blocks it flattens have dimensions that fit together.
  • ArrayFlatten can be used to form block matrices from arrays of blocks.
  • For a matrix of matrices, ArrayFlatten[a] yields a matrix whose elements are in the same order as in MatrixForm[a].
  • ArrayFlatten[a] is normally equivalent to Flatten[a,{{1,3},{2,4}}]. »
  • ArrayFlatten[a,r] is normally equivalent to Flatten[a,{{1,r+1},{2,r+2},,{r,2r}}].
  • For a tensor with rank 2r, ArrayFlatten[a,r] gives a tensor with rank r.
  • In ArrayFlatten[{{m11,m12,},{m21,m22,},}], all the matrices mi j in the same row must have the same first dimension, and matrices mi j in the same column must have the same second dimension.
  • In general, in ArrayFlatten[a,r], all the k^(th) dimensions of a[[i1,i2,,i_r]] must be equal for each possible value of ik .
  • Elements at level r whose array depth is less than r are treated as scalars, and are replicated to fill out a rank-r array of the appropriate dimensions.
  • ArrayFlatten works with SparseArray objects. »

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Create a block matrix by flattening out a matrix of matrices:

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Click for copyable input

Use 0s to represent zero matrices:

Click for copyable input
Click for copyable input
Introduced in 2007