Mathematica indices as variables

[Qubix]

1. I'll post here a simplified version of my problem

Say you have a matrix A, and you want all its components to be functions, for example:

A11 = Sin(a_n)
A12 = Cos(a_n)
A21 = Sin(b_n)
A22 = Cos(b_n)

And I want to be able to do this in mathematica so as to have the matrix A a function of n.

Homework Equations

How can I do this, such that when I ask

MatrixForm[A[4]] for example, it would give me the matrix with all components in terms of a_4 and b_4 ?

The Attempt at a Solution

Rather long and wrong, so better not post it here.

 

[DrClaude]

A[n_] := {{Sin[a[n]], Cos[a[n]]}, {Sin[b[n]], Cos[b[n]]}}

 

[Qubix]

Thanks for that DrClaude, it worked :)

PS:

Why won't Mathematica allow me to write:

(R[p_] := {{p/2, 0, 0, p/2}, {0, 1 - p, 0, 0}, {0, 0, 0, 0}, {p/2, 0, 0, p/2}}) // MatrixForm

It gives the error:

SetDelayed::write: "Tag List in {{p/2,0,0,p/2},{0,1-p,0,0},{0,0,0,0},{p/2,0,0,p/2}}[p_] is Protected.

 

[Bill Simpson]

It looks like you have already assigned that list to R. Try clearing the value of R and then try this again.

 

[rezeew]

I can suggest a solution to this problem using Mathematica's indexing functionality. Instead of using individual variables for each component of the matrix, we can define a function that takes the index as an argument and returns the desired value. For example:

A[n_] := {{Sin[a[n]], Cos[a[n]]}, {Sin[b[n]], Cos[b[n]]}}

This way, when we call A[4], we will get the matrix with all components in terms of a_4 and b_4. We can also use the MatrixForm function to display the matrix in a more organized format.

Furthermore, we can use Mathematica's Table function to generate a list of matrices for different values of n. For example:

Table[A[n], {n, 1, 10}]

This will generate a list of 10 matrices, each with its components in terms of a_n and b_n.

I hope this helps with your problem. Good luck!