eigv

Purpose

Computes eigenvalues and eigenvectors of a general matrix.

Format

{ lambda, v } = eigv(x)
Parameters:

x (NxN matrix or KxNxN array) – data used to compute the eigenvalues and eigenvectors.

Returns:
  • lambda (Nx1 vector or KxNx1 array) – the eigenvalues of x.
  • v (NxN matrix or KxNxN array) – the eigenvectors of x.

Examples

x = {  0.5  1.2  0.3,
       0.6  0.9  0.2,
       0.8  1.5  0.0 };

{ lambda, v } = eigv(x);

After the above code:

          1.8626          0.5044  -0.7122  -0.6152
lambda = -0.1871     v =  0.4317   0.3520   0.1361
         -0.2754          0.5643   0.2234   1.0458

Remarks

If x is an array, lambda will be an array containing the eigenvalues of each 2-dimensional array described by the two trailing dimensions of x, and v will be an array containing the corresponding eigenvectors. For example, if x is a 10x4x4 array, lambda will be a 10x4x1 array containing the eigenvalues and v a 10x4x4 array containing the eigenvectors of each of the 10 4x4 arrays contained in x.

Errors

If the eigenvalues cannot all be determined, lambda[1] is set to an error code. Passing lambda[1] to the scalerr() function will return the index of the eigenvalue that failed. The eigenvalues for indices scalerr(lambda[1])+1 to \(N\) should be correct. The eigenvectors are not computed.

Error handling is controlled with the low bit of the trap flag.

trap 0 set lambda[1] and terminate with message
trap 1 set lambda[1] and continue execution

Invalid inputs, such as an \(\infty\), missing value or Nan will cause an error. If the trap is set to 1, lambda will be set to a scalar error code and program execution will continue. Passing this scalar error code to the scalerr() function will return -1.

Eigenvalue ordering

The eigenvalues are unordered except that complex conjugate pairs of eigenvalues will appear consecutively with the eigenvalue having the positive imaginary part first. The columns of v contain the eigenvectors of x in the same order as the eigenvalues. The eigenvectors are not normalized.

See also

Functions eig(), eigh(), eighv()