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Wolfram Language & System Documentation Center
ArraySimplify
  • See Also
    • ArrayExpand
    • Simplify
    • TensorExpand
    • TensorReduce
  • Related Guides
    • Symbolic Vectors, Matrices and Arrays
    • 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[expr,assum]

simplifies using assumptions assum.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Multilinear Operations  
Array Operations  
Matrix Operations  
Vector Operations  
Options  
Assumptions  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • ArrayExpand
    • Simplify
    • TensorExpand
    • TensorReduce
  • Related Guides
    • Symbolic Vectors, Matrices and Arrays
    • See Also
      • ArrayExpand
      • Simplify
      • TensorExpand
      • TensorReduce
    • Related Guides
      • Symbolic Vectors, Matrices and Arrays

ArraySimplify

ArraySimplify[expr]

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

ArraySimplify[expr,assum]

simplifies using assumptions assum.

Details and Options

  • 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.

Examples

open all close all

Basic Examples  (3)

Simplify symbolic array expressions:

Use assumptions to specify dimensionality of variables:

Simplify expressions involving MatrixSymbol and VectorSymbol:

Scope  (42)

Multilinear Operations  (12)

Elementwise products of linear combinations:

Dot products of linear combinations:

ArrayDot products of linear combinations:

TensorProduct of linear combinations:

KroneckerProduct of linear combinations:

TensorWedge of linear combinations:

Cross product of linear combinations:

Tr of linear combinations:

TensorContract of linear combinations:

HodgeDual of linear combinations:

Transpose of linear combinations:

ConjugateTranspose of linear combinations:

Array Operations  (10)

Transpose, Conjugate and ConjugateTranspose:

Simplifications of TensorProduct:

Simplifications of TensorWedge:

Tr of Transpose, Conjugate and ConjugateTranspose:

Conjugate of array operations:

Conjugate and ConjugateTranspose of elementary functions:

Transpose of Listable mathematical functions:

Dot product of TensorProduct:

Commutativity of scalar-valued ArrayDot:

Simplifications of SymbolicIdentityArray:

Matrix Operations  (16)

Inverse:

PseudoInverse:

Adjugate:

MatrixPower:

Inverse, MatrixPower, PseudoInverse and Adjugate of a scalar multiple:

Inverse and Adjugate of Dot products:

Transpose, Conjugate and ConjugateTranspose of Inverse, Adjugate and PseudoInverse:

Transpose, Conjugate and ConjugateTranspose of MatrixPower:

Transpose, Conjugate and ConjugateTranspose of MatrixExp:

Transpose and ConjugateTranspose of Dot products:

Negative exponent MatrixPower of a Dot product:

Tr of Dot products:

Det composed with matrix operations:

Det of Dot products:

Matrix operations with KroneckerProduct arguments:

MatrixExp:

Vector Operations  (4)

Transpose of a vector:

Dot products of vectors and matrices:

Transpose of KroneckerProduct:

Cross products:

Options  (1)

Assumptions  (1)

Specify assumptions using the assumptions argument:

Use the Assumptions option:

Use Assuming to specify default assumptions:

Applications  (1)

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

Define the cost function:

Compute the gradient:

Simplify the gradient:

Properties & Relations  (2)

ArraySimplify performs only array transformations:

Simplify performs other transformations as well:

Use Assuming to propagate assumptions:

Possible Issues  (1)

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

Use assumptions to specify that c is a scalar:

See Also

ArrayExpand  Simplify  TensorExpand  TensorReduce

Related Guides

    ▪
  • Symbolic Vectors, Matrices and Arrays

History

Introduced in 2025 (14.2)

Wolfram Research (2025), ArraySimplify, Wolfram Language function, https://reference.wolfram.com/language/ref/ArraySimplify.html.

Text

Wolfram Research (2025), ArraySimplify, Wolfram Language function, https://reference.wolfram.com/language/ref/ArraySimplify.html.

CMS

Wolfram Language. 2025. "ArraySimplify." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArraySimplify.html.

APA

Wolfram Language. (2025). ArraySimplify. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArraySimplify.html

BibTeX

@misc{reference.wolfram_2025_arraysimplify, author="Wolfram Research", title="{ArraySimplify}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ArraySimplify.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_arraysimplify, organization={Wolfram Research}, title={ArraySimplify}, year={2025}, url={https://reference.wolfram.com/language/ref/ArraySimplify.html}, note=[Accessed: 01-December-2025]}

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