EIGENVALUES - created from Mind Map

Seite 1

Possess

can be used to compute determinants

are related to

have

can be

are special numbers which satisfy

Important features of their matrix

sum of eigenvalues equals the matrix trace

if there is a zero eigenvalue, then the matrix must be SINGULAR

Product of eigenvalues equals the matrix determinant

EIGENVECTORS

Comprise

are related matrices possess interesting properties such as

are special vectors associated with a matrix and its eigenvalues which satisfy

Eigenspace

which is the vector space composed of every linear combination of the eigenvector corresponding to a specific eigenvalue

if A is invertible, then its inverse matrix has the same eigenvectors with different associated eigenvalues 1/lamda

algebraic multiplicity

geometric multiplicity

the number of times a particular eigenvalue appears in the solution set of the characteristic polynomial

the dimension of the eigenvalue's corresponding eigenspace

real or complex number

which solve

the characteristic polynomial

which is