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Mathematica > Core Language > Expressions > Structural Operations on Expressions >

Join

Join[list₁, list₂, ...]
concatenates lists or other expressions that share the same head.

Join[list₁, list₂, ..., n]
joins the objects at level n in each of the list_i.

Join works on SparseArray objects by effectively concatenating the corresponding ordinary lists. »

Join[list₁, list₂, ..., n] handles ragged arrays by effectively concatenating all successive elements at level n in each of the list_i. »

Infix syntax:

Infix syntax:

Join two matrices to make longer columns:

Join columns of two matrices to make longer rows:

With ragged arrays successive elements are effectively concatenated:

The second row comes from the concatenation of nothing with {3,4}:

Join depth 3 arrays at different levels:

Join expressions with any head:

Join works with SparseArray objects:

Augment a matrix by adding a row:

Augment by a column:

Make a block matrix:

This can also be done with ArrayFlatten:

Join[list₁, list₂, ...]is equivalent to Flatten[{list₁, list₂, ...}, 1]:

Successively double a list by joining to itself:

Build up the Thue-Morse sequence: [more info]: