ArrayExpand [expr]
expands out symbolic array operations in expr.
ArrayExpand [expr,assum]
expands using assumptions assum.
ArrayExpand
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:
-
- You can specify default assumptions for ArrayExpand using Assuming .
Examples
open all close allBasic Examples (3)
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:
Det composed with matrix operations:
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:
Related Guides
History
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]}