SymbolicIdentityArray

SymbolicIdentityArray[{n1,n2,…}]

represents an n1×n2×…×n1×n2×… array with elements ai1,i2,…,j1,j2,… equal to 1 if all ikjk, and 0 otherwise.

Details

  • Valid dimension specifications ni in SymbolicIdentityArray[{n1,n2,…}] are positive integers. It is also possible to work with symbolic dimension specifications.
  • SymbolicIdentityArray may be produced by differentiation involving ArraySymbol objects.
  • For an array a=SymbolicIdentityArray[{n1,n2,…}] with positive integer dimension specifications ni, Normal[a] converts a to an explicit array. SparseArray[a] converts a to a SparseArray.

Examples

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Basic Examples  (2)

The derivative of a symbolic array variable with respect to itself is a SymbolicIdentityArray:

Create a SymbolicIdentityArray with explicit numeric dimensions:

Convert a to an explicit array:

Convert a to a SparseArray:

Scope  (2)

Arithmetic operations:

Array operations:

Properties & Relations  (5)

SymbolicIdentityArray gives a symbolic representation of the array:

Use Normal to convert a to an explicit array:

IdentityMatrix[n] gives an explicit version of SymbolicIdentityArray[{n}]:

SymbolicIdentityArray is a special case of SymbolicDeltaProductArray:

The derivative of a symbolic array variable with respect to itself is a SymbolicIdentityArray:

SymbolicIdentityArray objects are identity elements for ArrayDot:

Wolfram Research (2024), SymbolicIdentityArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html.

Text

Wolfram Research (2024), SymbolicIdentityArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html.

CMS

Wolfram Language. 2024. "SymbolicIdentityArray." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html.

APA

Wolfram Language. (2024). SymbolicIdentityArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html

BibTeX

@misc{reference.wolfram_2024_symbolicidentityarray, author="Wolfram Research", title="{SymbolicIdentityArray}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_symbolicidentityarray, organization={Wolfram Research}, title={SymbolicIdentityArray}, year={2024}, url={https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html}, note=[Accessed: 21-December-2024 ]}