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^(th) 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. »
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