Details

Indexed can be used to indicate components of symbolic vectors, matrices, tensors, etc.
When expr is a list, Indexed[expr,i] gives expr[[i]].
When expr is a list, Indexed[expr,{i,j,…}] gives Indexed[expr[[i]],{j,…}].

Examples

Represent part 1 of a symbolic vector x:

Wolfram Language code: Indexed[x, 1]

For a concrete vector, it extracts the part:

Wolfram Language code: Indexed[{a, b}, 1]

Represent part 1,2 in a symbolic matrix x:

Wolfram Language code: Indexed[x, {1, 2}]

For a concrete matrix, it extracts the part:

Wolfram Language code: Indexed[{{a, b, c}, {d, e, f}}, {1, 2}]

Use Indexed to work with symbolic vector variables:

Wolfram Language code: Integrate[Indexed[x, 1]^2Indexed[x, 2]^2, x∈Rectangle[]]

Wolfram Language code: Minimize[{Norm[x], Indexed[x, 1] + Indexed[x, 2] ≤ 1}, x∈Ball[]]

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