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:
“The strong sunlight, the wind from the sea,
all the conditions of its existence,
may have flaked off the paint, if ever it was painted,
and made it homelier than it was.”
—Elizabeth Bishop (1911–1979)