Eigen

One of the types of objects in Praat. An object of type Eigen represents the eigen structure of a square matrix, i.e. it contains the eigenvalues and their corresponding eigenvectors.

If the eigenvalues are real, which is mostly the case, the eigenvalues and their corresponding eigenvectors are always sorted. The default sorting order is descending, i.e. from large to small. The sorting order can be changed to ascending order by using the Sort command.

For complex eigenvalues there is no preferred sorting order. However, because complex eigenvalues always occur in pairs with equal real and opposite imaginary parts, i.e. a + i b and a - i b, the one with positive imaginary value always occurs first.

Inside an Eigen

With Inspect you will see the following attributes:

numberOfEigenvalues
the number of eigenvalues and eigenvectors
dimension
the dimension of an eigenvector.
eigenvalues[1..numberOfEigenvalues]
the real part of the eigenvalues.
eigenvectors[1..numberOfEigenvalues] [1..dimension]
the real parts of the eigenvectors, stored by row.
onlyReals
is true if all eigenvalues are real and false if not.
eigenvalues_im[1..numberOfEigenvalues]
the imaginary part of the eigenvalues.
eigenvectors_im[1..numberOfEigenvalues] [1..dimension]
the imaginary parts of the eigenvectors, stored by row.

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