# Questions tagged [operators]

Questions about using or composing operators--functional mappings from one state or vector space to another.

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### Construct a univariate function pertaining to the space of $2 \times 2$ real matrices [closed]

Consider the space of uniformly distributed $2 \times 2$ real matrices \begin{equation} \left( \begin{array}{cc} a & b \\ c & d \\ \end{array} \right), \end{equation} with the restriction ...
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### Custom operator form for system functions?

There are some functions for which an operator form would make sense but isn't implemented. For example, I'd like to make this work: RandomSample @ Range ...
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### What are rules in Mathematica and what are its uses? [closed]

I'm new to Mathematica. I have been going through the official reference and came across this article on rules to which I was led by a Google search on how to ...
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### Gâteaux (directional) derivatives and higher order differentials of a functional

I would like to calculate the Gâteaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
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### Defining a matrix with elements acting as operators

This question is directly related with my previous one. I'll try to be more specific here. I have a matrix {{a[x],b},{c,d}}, where ...
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### Replacing multiplication of matrix elements by application of these elements as functions

I want to realize the following idea in Mathematica. I've got a matrix {{a,b},{c,d}} which is multiplied to a vector {h,k} ...
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### what do those signs #1, #1^2, #1^3, & mean here? [duplicate]

I have read common pitfalls page and the documentation page but I still don't understand what do those signs mean here? ...
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### General function for the expansion of a polynomial of operators

This question is motivated by a Quantum mechanical problem - but in explaining the problem - I assume no knowledge of quantum mechanics. I want to define a function that can expand and simplify the ...
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### How best to write an exponential of differential operators?

I want to evaluate a term like this, $$\left.\exp\left({1\over 2}\sum_{i,j=1}^{n}(A^{-1})_{ij}{\partial \over \partial x_i}{\partial \over \partial x_j}\right) f(\vec{x})\right|_{\vec{x}=0}$$ and I ...
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### Differential equations expressed in operator form [duplicate]

Is it possible to make a workable operator representation of differential equations in Mathematica? I think it would make solving my differential equations easier, but I have no idea how to do it. ...
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### How to get Burgers hierarchy for any value of n

The Burgers hierarchy is defined by D[u[t, x], t] + α D[((∂/∂x) + u[t, x])^n u[t, x], x] How can I get the equation for the value of ...
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### Products of Differential Operators

I have a differential equation defined as the product of operators which I want to expand out into a polynomial in powers of $z\frac{d}{dz}$ $\qquad \prod_{n=1}^p(z\frac{d}{dz}+a_n)$ However when I ...
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### V10's Operator Forms - what are they good for?

V10 introduces an operator form for several functions perhaps primarily due to their role in queries as part of introducing data science functionality. At first pass it seems a lot of effort to add ...
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### How to define a non-standard algebra in Mathematica?

I want to define an algebra, where there are three elements: 0, 1 and $\infty$ and two operations, addition and multiplication defined, both commutative: \begin{align*} 0+0&=0\\ 0+1&=1\\ ...
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### Operator product

I have this problem: I define the gradient operator as: gradiente = {D[#, x] &, D[#, y] &, D[#, z] &} Now, if I want to apply the operator on a ...
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### Not commuting operator calculation

I am working on some operator calculation; I do not want the commutation relation. so xy ≠ yx. I found the mathematica code from https://reference.wolfram.com/language/ref/NonCommutativeMultiply....
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### Question about Rules and Pattern (The operator patt/;test)

Maybe this question is so trivial but it has confused me. I'm studying the What the @#%^&*?! do all those funny signs mean? and in the Rules and patterns under ...
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### Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
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### Define multilinear operator

In Maple it is possible to define a multilinear, orderless operator with: define(A,'orderless',multilinear): I can't seem to find the equivalent in Mathematica. ...
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### Why Drop and Take do not support a operator form

Since Mathematica 10 introduced the operator form, I have been a big fan of it. Whenever I use some buit-in functions, I first look up whether they support operator form. To me, it was quite ...
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### How to construct custom operators with precedence?

I need to combine data structures in operations analogous to addition, subtraction, multiplication and division (and more). I need more than one operation of each type, i.e. more than one method of ...
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### How to put a levelspec in operator form? [closed]

All variable argument functions need Function wrapped around them in operator form, but is there any other way to achieve this: ...
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### HoldForm[Operator ##] on some list

Recently in response to this question Mr.Wizard suggested an unusual way to summing numbers. This doesn't seem to be documented. ...
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### What happens when you divide by ##?

I've been playing around with sequences a bit. In particular with using ## with unary and binary operators. Let's start simple, the following all make some kind of ...
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### How is + as an infix operator associated with Plus?

How is + associated with Plus? Suppose I want to define a head FooBar and have it ...
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### Redefining a built-in operator

Is there a way I can redefine the || operator such that a||b will be 1/(1/a + 1/b)? Is it ...
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### How to write an operator that acts on pure function (to give another pure function)

I would like to write an operator oper that acts on a pure function f with an undetermined number of arguments, with the syntax <...
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### Expand a product of operators

Lets suppose I have a family of operators $f_i$, and unknown c-numbers $a,b,c$. I want to expand such products: $(f_1+f_2+c)(f_3+f_2+b)$ into $b c+b f_2+b f_1+c f_2+c f_3+f_2^2+f_1 f_2+f_2 f_3+f_1 f_3$...
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### How may I define e.g. Tilde[x,y] to have certain properties?

I would like to define, e.g., the Tilde[x,y] operator to have certain properties, and then investigate whether certain expressions involving that operator are True or not. For example, if I specify ...