# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# ArrayFlatten

ArrayFlatten[{{m11,m12,},{m21,m22,},}]
creates a single flattened matrix from a matrix of matrices .

ArrayFlatten[a,r]
flattens out r pairs of levels in the array a.

## DetailsDetails

• 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 in the same row must have the same first dimension, and matrices in the same column must have the same second dimension.
• In general, in ArrayFlatten[a,r], all the k dimensions of must be equal for each possible value of .
• 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:

 In[1]:=
 In[2]:=
 Out[2]=

Use 0s to represent zero matrices:

 In[1]:=
 In[2]:=
 Out[2]=