# ArraySymbol

ArraySymbol[a]

represents an array with name a.

ArraySymbol[a,{n1,n2,}]

represents an n1×n2× array.

ArraySymbol[a,{n1,n2,},dom]

represents an array with elements in the domain dom.

ArraySymbol[a,{n1,n2,},dom, sym]

represents an array with the symmetry sym.

# Details

• The name a in ArraySymbol[a,{n1,n2,},dom, sym] can be any expression.
• Valid dimension specifications ni in ArraySymbol[a,{n1,n2,},dom, sym] are positive integers. It is also possible to work with symbolic dimension specifications.
• Element domain specifications dom in ArraySymbol[a,{n1,n2,},dom, sym] include:
•  Complexes complex numbers Integers integers Reals real numbers NonNegativeReals real numbers x with x≥0 PositiveReals real numbers x with x>0
• Some symmetry specifications have names:
•  Symmetric[{s1,…,sn}] full symmetry in the slots si Antisymmetric[{s1,…,sn}] antisymmetry in the slots si
• In arithmetic and many other functions that work with lists, ArraySymbol objects do not automatically combine with other list arguments.
• Optimization functions, equation solvers and D recognize that ArraySymbol objects represent vector variables.

# Examples

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## Basic Examples(1)

Assign the value of the variable a to represent an mnp array with name "a":

Arithmetic operations recognize that a is not a scalar:

D recognizes that a is an array variable:

## Scope(4)

Compute derivatives with respect to an array variable:

Compute derivatives involving array-valued functions:

Use an array variable in optimization:

Solve equations and inequalities involving an array variable:

## Applications(3)

Derive a least-squares solution for data given as a list of pairs :

Find the vector of vertical deviations for the data:

Define the sum of squares of the vertical deviations for the data:

Set up the least-squares equations:

Generate some data:

Solve the least-squares problem for this data:

Find an optimality condition for a portfolio optimization problem with the expected return and standard deviation :

The goal is to maximize when the vector of asset weights satisfies Total[x]=1. The constraint can be used to represent where the unconstrained vector variable consists of the first coordinates of :

The maximum occurs at a critical point of :

Express the condition in terms of :

Compute the gradient of the log-likelihood function of the linear regression model represented by the equation , where are normally distributed random variables with mean zero and variance :

The log-likelihood function is given by:

Compute :

Express the result in terms of :

Compute :

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_arraysymbol, author="Wolfram Research", title="{ArraySymbol}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ArraySymbol.html}", note=[Accessed: 15-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_arraysymbol, organization={Wolfram Research}, title={ArraySymbol}, year={2024}, url={https://reference.wolfram.com/language/ref/ArraySymbol.html}, note=[Accessed: 15-August-2024 ]}