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 ...
14
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2answers
277 views

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[3] @ Range[10] ...
3
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1answer
700 views

Hadamard Lemma and commutators algebra

I would like to implement the following formula, which goes under the name of Hadamard Lemma: $ e^A \, B \, e^{-A} = \sum_{k=0}^{+\infty} \frac{1}{k!} [A,B]_k $ where $ [A,B]_0 = B , \...
2
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1answer
7k views

Difference between = and := [duplicate]

I wanted to know the difference between two operators: = and := I couldn't find the ":=" operator on the list at https://reference.wolfram.com/language/tutorial/Operators.html Can someone help? ...
10
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3answers
4k views

Using D to find a symbolic derivative

I need to do the following: Define a function Take the derivative of this function and have a look at the symoblic representation Substitute in some values With the bonus that I want to use the ...
4
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1answer
638 views

What does “slash at” mean /@? [closed]

I searched "slash at" as well as "/@" to no avail. Consider Normalize /@ A I see the net effect, but what does /@ really mean? I understand that @ can be used ...
1
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0answers
51 views

Operator Splitting and Taylore series

I am not a user of mathematica so I am not sure if what I want to do is possible. Imagine I have the following cauchy problem: $$\frac{dw}{dt} = F(t, w(t)) = f1(w(t), t) + f2(w(t), t)$$ where I have ...
3
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1answer
100 views

Generating a list of values from the application of a sequence of operators

I have a module 'L' that reads: L[f0_,n_]:=Module[{ft=f0}, a[t]={}; Do[AppendTo[a[t], Inr[f0,ft]]; ft=U@ft, {n}]]; It takes an input function f0, applies ...
34
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3answers
790 views

Is there a comprehensive list of functions with operator forms?

As of version 10, Mathematica sports operator forms for many functions like Map, SortBy, ...
3
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2answers
178 views

Product of n different operators

I have a sequence of differential operators given by $H_n = x \frac{d}{dx} + n$ where $n=1,2,...$ and I would like to construct the operator $\hat{O}(n) = \frac{1}{n!}H_nH_{n-1}...H_2H_1$ as a ...
5
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1answer
1k views

I want to be able to define (a(x) d/dx + b(x))^n

I want to be able to define an operator $(a(x) d/dx + b(x))^n$ where $d/dx$ is the derivative operator and $a(x)$ and $b(x)$ are known functions and $n$ is a positive integer. Related Query: How ...
0
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0answers
355 views

Non commutative products and scalars

Say I have an expression such as $$a.(\alpha b)$$ where $a$ and $b$ are non-commutative operators, but $\alpha$ is simply a scalar. How do I tell Mathematica to treat $\alpha$ as a scalar and "pull" ...
1
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1answer
162 views

How to do matrix operation if the first matrix is an operator? [duplicate]

Suppose I have: mM = {{D[#, x]&, D[#, y]&}, {D[#, y]&, D[#, z]&}} v = {f[x, y, z], g[x, y, z]} I want to get $u=mMv=\{\frac{\partial f}{\partial ...
1
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1answer
85 views

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 ...
3
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1answer
699 views

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: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
4
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1answer
425 views

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 ...
3
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2answers
209 views

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} ...
5
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4answers
5k views

How to write a differential operator in Mathematica

I have a very basic question. I am trying to code the LHS of the differential equation: $$\Big[\frac{1}{\sin\theta}\frac{d}{d\theta}\big(\sin\theta\frac{d}{d\theta}\big)-\frac{m^2}{\sin^2\theta}+n(n+...
2
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2answers
115 views

Why is the square of a differential operator not evaluated automatically?

I defined an operator: py[f_[x, y]] := (I*h*D[f[x, y], y] - x) // Expand (not important, but it represents a simplified component of a quantum momentum in a ...
7
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1answer
643 views

Define an operator with the distributive property

I would like to define the operator with distributive, associative, and commutative properties - so that Mathematica can symbolically simplify expressions I use ...
3
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2answers
148 views

Computing powers of the operator using symbolic computation

Suppose $t\in\mathbb{R_+}$ - some parameter, $V: \mathbb{R}\to\mathbb{R}$ - some function. I have an operator $S:f\mapsto S[f]$ that maps a function $f$ to a function $S[f]$: $$ S[f](x) = f(x+\sqrt{t})...
0
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1answer
562 views

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? ...
3
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3answers
339 views

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 ...
5
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2answers
536 views

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 ...
0
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1answer
135 views

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. ...
1
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1answer
88 views

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 ...
4
votes
1answer
260 views

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 ...
65
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6answers
3k views

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 ...
15
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2answers
2k views

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\\ ...
2
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1answer
167 views

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 ...
2
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1answer
606 views

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....
10
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1answer
371 views

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 ...
4
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0answers
772 views

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]] ...
10
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1answer
297 views

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. ...
8
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1answer
249 views

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 ...
7
votes
1answer
512 views

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 ...
0
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1answer
81 views

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: ...
7
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2answers
334 views

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. ...
17
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2answers
1k views

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 ...
25
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3answers
2k views

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 ...
8
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3answers
525 views

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 ...
7
votes
5answers
652 views

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 <...
2
votes
1answer
165 views

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 $b c+b f_2+b f_1+c f_2+c f_3+f_2^2+f_1 f_2+f_2 f_3+f_1 f_3$...
0
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2answers
235 views

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 ...
0
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1answer
468 views

Symbolic matrix calculation [closed]

I have question about a matrix calculation like $\mathbf{b}^{t}\,\Sigma\,\mathbf{b}$, where $\Sigma$ is a 7 by 7 matrix, and $\mathbf{b}$ is vector of 7 elements, and each element in the vector $\...
5
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1answer
180 views

Can Mathematica Operators be combined in a linear fashion for readability? [duplicate]

Here's a simple example. Suppose we want to find the off-diagonal matrix of m: m={{1,2},{3,4}} This can be solved fairly simply by extracting a list of the ...
10
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2answers
6k views

Defining quantum-mechanical Bra and Ket operations

I have the following ket in the Fock basis: $\vert3, 0 ,1\rangle$, where each entry defines the number of photons in a particular mode and can take any one of the following numbers: 0, 1, 2, 3. As a ...
5
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0answers
123 views

Operator which can be interpreted as binary and unary

I'm a bit lost with the way how e.g. the + operator is implemented in Mathematica as binary (infix) and unary (prefix) operator depending on the context, since I would like to define a similiar ...
3
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1answer
191 views

Cannot normally underline slash characters and hyperlinks

Really, if you evaluate Style["/", Underlined] or type / and set the font of the character to be underlined through Format|Font..., you get $/$, not $\underline{/}$....
7
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2answers
808 views

How to make a binary function associative? (Or define an n-ary function?)

Suppose I have a simple function that I assign to an operator f[a_, b_] := a + b CirclePlus = f Then I want to write ...