Finding Eigenvalues of Real Non-Symmetric Matrices

In summary, an eigenvalue is a scalar value that represents how a linear transformation changes the direction of a vector. The most commonly used method for finding eigenvalues of a real non-symmetric matrix is the QR algorithm, which involves decomposing the matrix into a product of two matrices and using iterations to approximate the eigenvalues. A real non-symmetric matrix can have complex eigenvalues due to the complex roots of its characteristic polynomial. The number of eigenvalues of a real non-symmetric matrix is equal to its dimension, and there are special properties such as complex conjugate pairs and the relationship between eigenvalues and the trace and determinant of the matrix.
  • #1
gradnu
21
0
Hi,
Can somebody provide a link(other than numerical recipes) where I can get an optimized 'C' program for calculating eigenvalues of real nonsymmetric martix.

Thanks
 
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  • #2
What's wrong with Numerical Recipes?

- Warren
 
  • #3
The license? ;)

@gradnu
Try google? Or write your own?
 
  • #5
Thanks
 

1. What is an eigenvalue?

An eigenvalue is a scalar value that represents how a linear transformation changes the direction of a vector. In other words, it is a value that, when multiplied by a vector, produces a new vector that is parallel to the original vector.

2. How do you find eigenvalues of a real non-symmetric matrix?

The most commonly used method for finding eigenvalues of a real non-symmetric matrix is the QR algorithm. This method involves decomposing the matrix into a product of two matrices, Q and R, and then using a series of iterations to approximate the eigenvalues.

3. Can a real non-symmetric matrix have complex eigenvalues?

Yes, a real non-symmetric matrix can have complex eigenvalues. This is because the eigenvalues of a matrix are determined by the characteristic polynomial, which can have complex roots even if the matrix is real.

4. How do you determine the number of eigenvalues of a real non-symmetric matrix?

The number of eigenvalues of a real non-symmetric matrix is equal to the dimension of the matrix. This means that an n x n matrix will have n eigenvalues.

5. Are there any special properties of eigenvalues for real non-symmetric matrices?

Yes, there are a few special properties of eigenvalues for real non-symmetric matrices. For example, the eigenvalues of a real non-symmetric matrix are always complex or occur in complex conjugate pairs. Additionally, the sum of the eigenvalues of a real non-symmetric matrix is equal to the trace of the matrix, and the product of the eigenvalues is equal to the determinant of the matrix.

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