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:
-
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
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 GenerateConditionsFalse, argument dimensions are quietly assumed to satisfy equations necessary for the expression to be well defined:
With GenerateConditionsTrue, the necessary conditions are given explicitly:
Properties & Relations (1)
Use NonCommutativeExpand to expand general noncommutative polynomials:
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