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ArraySimplify—Wolfram Language Documentation

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• See Also
  • ArrayExpand
  • Simplify
  • TensorExpand
  • TensorReduce
• Related Guides
  • Symbolic Vectors, Matrices and Arrays

ArraySimplify[expr]

performs a sequence of array transformations on expr and returns the simplest form it finds.

• ArraySimplify can be used for simplifying symbolic array expressions.
• ArraySimplify makes use of multilinearity of array operations, as well as of numerous array, matrix and vector operation identities.
• Dimensionality of symbolic arguments can be specified through assumptions or by using ArraySymbol, MatrixSymbol or VectorSymbol.
• Symbolic arguments of unspecified dimensionality are assumed to be arrays of dimensions appropriate for the functions they are used in. In multi-argument Listable functions, like Plus or Times, all arguments are assumed to have the same dimensions unless specified differently. »
• ArraySimplify has the option Assumptions, specifying default assumptions to be appended to assum.
• The default setting for the Assumptions option is $Assumptions.
• You can specify default assumptions for ArraySimplify using Assuming.
• Complexity of each form generated is assessed using a measure similar to LeafCount, except that ArraySymbol, MatrixSymbol, VectorSymbol, SymbolicZerosArray, SymbolicOnesArray, SymbolicIdentityArray and SymbolicDeltaProductArray subexpressions are treated as atoms.

Simplify symbolic array expressions:

Use assumptions to specify dimensionality of variables:

Simplify expressions involving MatrixSymbol and VectorSymbol:

Specify assumptions using the assumptions argument:

Use the Assumptions option:

Use Assuming to specify default assumptions:

Derive a formula for the gradient of the least-squares cost function:

Define the cost function:

Compute the gradient:

Simplify the gradient:

Symbolic arguments of unspecified dimensionality are not assumed to be scalars:

Use assumptions to specify that c is a scalar:

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