How to extract a factor out of a matrix?

Forum Attachments

How to extract a factor out of a matrix?

Taubi (guest) 12 Jan 2016 11:48

Hi at all,

I think my problem is simple, at least: I want to extract a common factor or a common denom out of a matrix to simplify it.

Just an example: I want

(1)

\begin{pmatrix} \frac{1}{20} & \frac{1}{20} & \frac{1}{10} \\ \frac{3}{20} & \frac{1}{10} & \frac{1}{20} \\ \frac{1}{5} & \frac{1}{20} & \frac{3}{20} \end{pmatrix}

to simplify to

(2)

\begin{align} \frac{1}{20} &\begin{pmatrix} 1 & 1 & 2 \\ 3 & 2 & 1 \\ 4 & 1 & 3 \end{pmatrix} \end{align}

I tried severel commands like $factor()$ or $expand()$, but I didn't solve the issue.

May someone could help me? - Thanks!

Re: How to extract a factor out of a matrix?

Michael2_3B 15 Jan 2016 15:33

As I do not own an Nspire, I don't know how. However, I was able to make a TI-Basic program on the 83+/84+ calculators. It uses the matrix [B] as the matrix with your original values. Note, this is not the most optimized, but it should work for any size matrix.

dim([B]
Ans(1→A
dim([B]
Ans(2→B
[B](1,1→M
For(I,1,B
 Matr▶list([B],I,A
 min(M,min(⌊A→M
End
For(I,1,A
 For(N,1,B
  [B](I,N)/M→[B](I,N
 End
End
Disp M
Disp "*
Pause [B]

For your starting matrix, just create a matrix in [B] that is however wide by however tall, then enter your values, and then run the program, and the program will show you the common factor (or whatever) multiplied by the new, simplified matrix, like you showed above.

Like I said, I don't know how you would do this on Nspire, but this works for 83+/84+ for sure.

Last edited on 15 Jan 2016 17:54 by Michael2_3B Show more

Re: How to extract a factor out of a matrix?

Firts Glimphs 17 Jun 2016 19:50

This one is in Nspire BASIC, leveraging inbuilt Nspire functions. Edit: I've now verified this code in the emulator within TI's Student Software.

Define matCF(mat) = Prgm
Local i, j, k, maxcd, tempcd, denoms
denoms := getDenom(mat▶list(mat))
maxcd := 1
tempcd := 1
k := dim(denoms)
For i, 1 , k - 1
  For j, i + 1, k
    tempcd := lcm(denoms[i], denoms[j])
    If tempcd > maxcd Then
      maxcd := tempcd
    EndIf
  EndFor
EndFor
Disp 1 / maxcd, mat * maxcd
EndPrgm

This will display the greatest common fractional factor, less than or equal to one, of all values in the matrix, alongside the matrix with that factor divided out of every value.

Last edited on 18 Jun 2016 03:57 by Firts Glimphs Show more