eigenvalues's Usage Examples:

For a matrix, eigenvalues and eigenvectors can be used to decompose the matrix—for example by diagonalizing it.

a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.

principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces.

may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions.

M is symmetric or Hermitian, and all its eigenvalues are real and positive (resp.

share a property with real symmetric matrices of always having real eigenvalues.

circumstances, the question may be reduced to a well-studied problem involving eigenvalues of matrices.

spectrum of a heavy atom nucleus should resemble the spacings between the eigenvalues of a random matrix, and should depend only on the symmetry class of the.

The trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities), and it is invariant with respect to a.

to which the matrix has the required form exists if and only if all eigenvalues of the matrix lie in K, or equivalently if the characteristic polynomial.

generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix.

necessarily distinct eigenvalues).

Decomposition: A = V D V − 1 {\displaystyle A=VDV^{-1}} , where D is a diagonal matrix formed from the eigenvalues of A, and the.

and the diagonal entries of D {\displaystyle D}  are the corresponding eigenvalues of T {\displaystyle T} ; with respect to this eigenvector basis, A {\displaystyle.

problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix.

Then, we compute the covariance matrix of the data and calculate the eigenvalues and corresponding eigenvectors of this covariance matrix.

The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph.

In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape.

a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.

} When b = 0, the eigenvalues of A determine the structure of the phase space.

From the eigenvalues and the eigenvectors of A it is possible.

Synonyms:

eigenvalue of a square matrix; value; eigenvalue of a matrix; characteristic root of a square matrix;

Antonyms:

disesteem; criticize; worthlessness; unimportance; importance;