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:

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)

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

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