# Make a triangular matrix from a square matrix

• quin
In summary, the user is seeking help in finding the eigenvalues of a complex 12x12 matrix using MATLAB or Mathematica. They have tried using QR decomposition, but it is not suitable for symbolic matrices. They are looking for alternative methods to solve the problem.
quin
dear users
I have a problem in finding eigenvalues of a 12*12 because the 12*12 matrix is so complicated
so i decided to first make my 12*12 matrix in form of upper triangular form but I don't know how can I do it with MATLAB or mathematica?
can you please tell me that what is the formula in MATLAB or mathematica for make an upper triangular matrix from my own 12*12 matrix?

thanks alot

Hello,

If you need to get the eigenvalues/eigenvectors, why don't you use the corresponding function, instead making the matrix diagonal?

Just thinking ...

J.

matlab and mathematica couldn't do it.matrix is very complex for these softwares and they cannot calculate eigenvalues of matrix

NemoReally said:
QR decomposition. http://en.wikipedia.org/wiki/QR_decomposition

Look up the function qr in Matlab and QRDecomposition in Mathematica. Is your matrix too complicated to post? Is it numeric or symbolic?

thank you for your guide but my matrix which I want to find its eigenvalue is symbolic and qr is for numeric matrix.

these are mathematica's and matlab's files of my matrix so that you can have a look on it.
thank you alot

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Last edited:
You want the symbolic solution for the eigenvalues of a 12x12 matrix?!

That would be a nightmare!

As far as I know, the various methods of computing eigenvalues--QR Decomposition, Characteristic Polynomial, etc.--are all pretty complicated. Perhaps the solutions of a 3x3 matrix would be nice concise answers. However, the solutions of a 12x12 matrix sure would not be.

## What is a triangular matrix?

A triangular matrix is a square matrix in which all the values above or below the main diagonal are zero. This means that the values form a triangle shape when plotted out.

## How do you create a triangular matrix from a square matrix?

To create a triangular matrix from a square matrix, you can either remove all the values below or above the main diagonal, or you can replace them with zeros. This will result in a triangular-shaped matrix.

## What is the purpose of creating a triangular matrix?

Creating a triangular matrix can help to simplify and speed up certain mathematical operations, such as matrix multiplication. Additionally, triangular matrices are often used in computer algorithms and data structures.

## Can a non-square matrix be turned into a triangular matrix?

No, a non-square matrix cannot be turned into a triangular matrix. Triangular matrices are only applicable to square matrices, where the number of rows is equal to the number of columns.

## Are there different types of triangular matrices?

Yes, there are two types of triangular matrices: upper triangular and lower triangular. Upper triangular matrices have zero values below the main diagonal, while lower triangular matrices have zero values above the main diagonal.

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