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SymbolicIdentityArray
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SymbolicIdentityArray

New in 14.1[Experimental]

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

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

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-vp0kt
In[2]:=2
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https://wolfram.com/xid/0mk1bi3vo1qy-vxjxp
Out[2]=2

Create a SymbolicIdentityArray with explicit numeric dimensions:

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-cfqmya
Out[1]=1

Convert a to an explicit array:

In[2]:=2
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https://wolfram.com/xid/0mk1bi3vo1qy-d2sqr7
Out[2]=2

Convert a to a SparseArray:

In[3]:=3
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https://wolfram.com/xid/0mk1bi3vo1qy-wr1qc
Out[3]=3

Scope  (2)Survey of the scope of standard use cases

Arithmetic operations:

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-i1mx3a
Out[1]=1

Array operations:

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-lunyjf
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mk1bi3vo1qy-coq16s
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0mk1bi3vo1qy-emy3gi
Out[3]=3

Properties & Relations  (5)Properties of the function, and connections to other functions

SymbolicIdentityArray gives a symbolic representation of the array:

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-z7pn2i
Out[1]=1

Use Normal to convert a to an explicit array:

In[2]:=2
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https://wolfram.com/xid/0mk1bi3vo1qy-4mh225
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-b651zf
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mk1bi3vo1qy-p2dtqe
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0mk1bi3vo1qy-kcbwdh
Out[3]=3

SymbolicIdentityArray is a special case of SymbolicDeltaProductArray:

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-60ex52
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0mk1bi3vo1qy-el9d6c
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0mk1bi3vo1qy-cakgwq
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0mk1bi3vo1qy-oziq7k
In[2]:=2
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https://wolfram.com/xid/0mk1bi3vo1qy-p0fjd4
Out[2]=2

SymbolicIdentityArray objects are identity elements for ArrayDot:

In[1]:=1
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https://wolfram.com/xid/0mk1bi3vo1qy-jl9lq8
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mk1bi3vo1qy-qpo695
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0mk1bi3vo1qy-mavstq
Out[3]=3
Wolfram Research (2024), SymbolicIdentityArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html.
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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.

✖
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.

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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

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

BibTeX

@misc{reference.wolfram_2025_symbolicidentityarray, author="Wolfram Research", title="{SymbolicIdentityArray}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html}", note=[Accessed: 15-April-2025 ]}

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@misc{reference.wolfram_2025_symbolicidentityarray, author="Wolfram Research", title="{SymbolicIdentityArray}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html}", note=[Accessed: 15-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_symbolicidentityarray, organization={Wolfram Research}, title={SymbolicIdentityArray}, year={2024}, url={https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html}, note=[Accessed: 15-April-2025 ]}

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@online{reference.wolfram_2025_symbolicidentityarray, organization={Wolfram Research}, title={SymbolicIdentityArray}, year={2024}, url={https://reference.wolfram.com/language/ref/SymbolicIdentityArray.html}, note=[Accessed: 15-April-2025 ]}