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ArrayExpand [expr]

expands out symbolic array operations in expr.

ArrayExpand [expr,assum]

expands using assumptions assum.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Multilinear Operations  
Array Operations  
Matrix Operations  
Vector Operations  
Simplifications  
Options  
Assumptions  
GenerateConditions  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page

ArrayExpand [expr]

expands out symbolic array operations in expr.

ArrayExpand [expr,assum]

expands using assumptions assum.

Details and Options

  • ArrayExpand can be used for expanding out symbolic array operations.
  • ArrayExpand 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. »
  • The following options can be given:
  • Assumptions $Assumptions default assumptions to be appended to assum
    GenerateConditions False whether to generate conditions on parameters
  • You can specify default assumptions for ArrayExpand using Assuming .

Examples

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Basic Examples  (3)

Expand out Dot product of sums of arrays:

Expand out Tr of a linear combination of arrays:

Expand out Inverse of Dot product of matrices:

Scope  (45)

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  (6)

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 :

Matrix Operations  (13)

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:

MatrixPower of a linear combination:

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:

Expressions involving MatrixExp :

Vector Operations  (4)

Transpose of a vector:

Canonicalize Dot products of vectors and matrices:

Transpose of KroneckerProduct :

Cross products:

Simplifications  (10)

Simplifications of Inverse :

Simplifications of PseudoInverse :

Simplifications of Adjugate :

Simplifications of MatrixPower :

Simplifications of Transpose , Conjugate and ConjugateTranspose :

Simplifications of SymbolicIdentityArray :

Simplifications of TensorProduct :

Simplifications of Cross :

Simplifications of TensorWedge :

Simplifications of MatrixExp :

Options  (2)

Assumptions  (1)

Specify assumptions using the assumptions argument:

Use the Assumptions option:

Use Assuming to specify default assumptions:

GenerateConditions  (1)

With the default setting GenerateConditions False , argument dimensions are quietly assumed to satisfy equations necessary for the expression to be well defined:

With GenerateConditions True , the necessary conditions are given explicitly:

Properties & Relations  (1)

Use NonCommutativeExpand to expand general noncommutative polynomials:

Specify names for addition and multiplication operations:

Possible Issues  (1)

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

Use assumptions to specify that c is a scalar:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_arrayexpand, author="Wolfram Research", title="{ArrayExpand}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ArrayExpand.html}", note=[Accessed: 17-November-2025]}

BibLaTeX

@online{reference.wolfram_2025_arrayexpand, organization={Wolfram Research}, title={ArrayExpand}, year={2025}, url={https://reference.wolfram.com/language/ref/ArrayExpand.html}, note=[Accessed: 17-November-2025]}

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