Defective Matrix - Jordan Block

Jordan Block

Any Jordan block of size 2×2 or larger is defective. For example, the n × n Jordan block,

J = \begin{bmatrix} \lambda & 1 & \; & \; \\ \; & \lambda & \ddots & \; \\ \; & \; & \ddots & 1 \\ \; & \; & \; & \lambda \end{bmatrix},

has an eigenvalue, λ, with multiplicity n, but only one distinct eigenvector,

Read more about this topic:  Defective Matrix

Famous quotes containing the words jordan and/or block:

    “We do not deride the fears of prospering white America. A nation of violence and private property has every reason to dread the violated and the deprived.”
    —June Jordan (b. 1939)

    “Dug from the tomb of taste-refining time,
    Each form is exquisite, each block sublime.
    Or good, or bad,—disfigur’d, or deprav’d,—
    All art, is at its resurrection sav’d;
    All crown’d with glory in the critic’s heav’n,
    Each merit magnified, each fault forgiven.”
    —Martin Archer, Sir Shee (1769–1850)