BUILT-IN MATHEMATICA 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:

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Use 0s to represent zero matrices:

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