Matrices With Conditions On Eigenvalues or Eigenvectors
| Name | Explanation | Notes |
|---|---|---|
| Companion matrix | A matrix whose eigenvalues are equal to the roots of the polynomial. | |
| Convergent matrix | A square matrix whose successive powers approach the zero matrix. | Its eigenvalues have magnitude less than one. |
| Defective matrix | A square matrix that does not have a complete basis of eigenvectors, and is thus not diagonalisable. | |
| Diagonalizable matrix | A square matrix similar to a diagonal matrix. | It has an eigenbasis, that is, a complete set of linearly independent eigenvectors. |
| Hurwitz matrix | A matrix whose eigenvalues have strictly negative real part. A stable system of differential equations may be represented by a Hurwitz matrix. | |
| Positive-definite matrix | A Hermitian matrix with every eigenvalue positive. | |
| Stability matrix | Synonym for Hurwitz matrix. | |
| Stieltjes matrix | A real symmetric positive definite matrix with nonpositive off-diagonal entries. | Special case of an M-matrix. |
Read more about this topic: List Of Matrices
Famous quotes containing the word conditions:
“My dear young friend ... civilization has absolutely no need of nobility or heroism. These things are symptoms of political inefficiency. In a properly organized society like ours, nobody has any opportunities for being noble or heroic. Conditions have got to be thoroughly unstable before the occasion can arise.”
—Aldous Huxley (1894–1963)