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:

“All of Western tradition, from the late bloom of the British Empire right through the early doom of Vietnam, dictates that you do something spectacular and irreversible whenever you find yourself in or whenever you impose yourself upon a wholly unfamiliar situation belonging to somebody else. Frequently it’s your soul or your honor or your manhood, or democracy itself, at stake.”
—June Jordan (b. 1939)

“Painting consumes labour not disproportionate to its effect; but a fellow will hack half a year at a block of marble to make something in stone that hardly resembles a man. The value of statuary is owing to its difficulty. You would not value the finest head cut upon a carrot.”
—Samuel Johnson (1709–1784)