Characteristic Polynomial - Examples

Examples

Suppose we want to compute the characteristic polynomial of the matrix

A=\begin{pmatrix} 2 & 1\\ -1& 0 \end{pmatrix}.

We must compute the determinant of

t I-A = \begin{pmatrix} t-2&-1\\ 1&t-0 \end{pmatrix} which is the characteristic polynomial of A.

Another example uses hyperbolic functions of a hyperbolic angle φ. For the matrix take

Its characteristic polynomial is

Read more about this topic:  Characteristic Polynomial

Famous quotes containing the word examples:

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)

    “In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
    —Michel de Montaigne (1533–1592)

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)