# Symbolic Vector Manipulation Software?

• daviddoria
In summary, the conversation is about the possibility of using software like Maple or Matlab to perform a derivative involving vectors. The desired outcome is to find a way to calculate (1/2)*A*x or (A+A^T)x using Maple or Matlab, but it is not clear how to do this. Suggestions and clarifications are requested.
daviddoria
I would like to do something like a derivative with respect to a vector or really anything involving a vector (of known dimension, but unknown values) going in and a vector coming out:

x= 4 by 1 vector
A = 4 by 4 matrix
diff( Transpose(x) * A * x, x)

should return (1/2)*A*x

Is there software that can do this? I am familiar with maple and matlab, but I don't think either of them can do this.

Any suggestions?

Thanks!

David

If A is symmetric it is $2Ax$, otherwise it is $(A+A^T)x$ ! And I don't understand why you can not do with Maple or MATLAB. Do you mean handling vector calculus?

ahh yea sorry 2Ax or (A+A^T)x is clearly correct.

So that is would I would like to do, either with Maple or Matlab. Does anyone know how?

Do what? The whole Maple is designed for this! Please, take the time for asking one exact question.

Here is one exact question. I want to do this:

with(LinearAlgebra);
b:=Vector(x,3);
B:=Matrix(A,3,3);
f:=Transpose(b)*B*b;
diff(f,b)

but i get:
Error, (in rtable/Product) invalid arguments
when defining f

Now, I see your point but I can't give you the exact code because I don't have Maple on this computer. But I can tell you that it should be also related with ">>with(VectorCalculus);". Also, it would surprise me if it works without setting the dimension to, say, "m". Sorry for this sloppy answer but I have to access to Maple first to give a correct answer.

trambolin, daviddoria, did you figure out the answer to this question? Thanks!

## 1. What is Symbolic Vector Manipulation Software?

Symbolic Vector Manipulation Software is a type of computer program that allows users to manipulate mathematical expressions involving vectors. It can perform operations such as vector addition, subtraction, and multiplication, as well as simplify and solve vector equations.

## 2. What are the benefits of using Symbolic Vector Manipulation Software?

One of the main benefits of using Symbolic Vector Manipulation Software is its ability to handle complex mathematical expressions involving vectors. It also allows for quick and accurate calculations, and can help users visualize vector operations through graphical representations.

## 3. Is Symbolic Vector Manipulation Software difficult to use?

The level of difficulty in using Symbolic Vector Manipulation Software may vary depending on the user's familiarity with mathematical concepts and the specific software being used. However, most software programs come with user-friendly interfaces and tutorials to help users get started.

## 4. Can Symbolic Vector Manipulation Software be used for real-world applications?

Yes, Symbolic Vector Manipulation Software is widely used in various fields such as physics, engineering, and computer graphics. It can be used to solve complex problems involving vectors in these fields, making it a valuable tool for real-world applications.

## 5. Are there any free options for Symbolic Vector Manipulation Software?

Yes, there are free and open-source options for Symbolic Vector Manipulation Software, such as Maxima and SymPy. These programs offer similar features to paid software and can be a good option for those on a budget or for educational purposes.

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