ArraySimplify [expr]
performs a sequence of array transformations on expr and returns the simplest form it finds.
ArraySimplify [expr,assum]
simplifies using assumptions assum.
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 allBasic 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 :
Adjugate :
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:
Det composed with matrix operations:
Matrix operations with KroneckerProduct arguments:
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
Related Guides
History
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: 17-November-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: 17-November-2025]}