• ← LeviCivitaTensor
• → RotationTransform

Outer

Outer product (WMA link)

Outer[f, x, y]

computes a generalised outer product of x and y, using the function f in place of multiplication.

• • Outer[f, {a, b}, {1, 2, 3}]

Outer product of two matrices:

• • Outer[Times, {{a, b}, {c, d}}, {{1, 2}, {3, 4}}]

Outer product of two sparse arrays:

• • Outer[Times, SparseArray[{{1, 2} -> a, {2, 1} -> b}], SparseArray[{{1, 2} -> c, {2, 1} -> d}]]

Outer of multiple lists:

• • Outer[f, {a, b}, {x, y, z}, {1, 2}]

Outer converts input sparse arrays to lists if f=!=Times, or if the input is a mixture of sparse arrays and lists:

• • Outer[f, SparseArray[{{1, 2} -> a, {2, 1} -> b}], SparseArray[{{1, 2} -> c, {2, 1} -> d}]]

• • Outer[Times, SparseArray[{{1, 2} -> a, {2, 1} -> b}], {c, d}]

Arrays can be ragged:

• • Outer[Times, {{1, 2}}, {{a, b}, {c, d, e}}]

Word combinations:

• • Outer[StringJoin, {"", "re", "un"}, {"cover", "draw", "wind"}, {"", "ing", "s"}] // InputForm

Compositions of trigonometric functions:

• • trigs = Outer[Composition, {Sin, Cos, Tan}, {ArcSin, ArcCos, ArcTan}]

Evaluate at 0:

• • Map[#[0] &, trigs, {2}]