Eigendecomposition, Eigenvalue, Eigenvector, Eigenfunction 特徵分解、特徵值、特徵向量、特徵函數/固有值、固有向量、固有函數

Eigendecomposition 特徵分解
Spectral decomposition 譜分解

scalar 純量
vector 向量

For n×n matrix A,

if Ax = λx

where
λ is a scalar.

x is a non-zero vector with dimension N.

Then

Av = λv
Eigenvalue 特徵值/固有值 λ
Eigenvector 特徵向量/固有向量 v

Af = λf
Eigenfunction 特徵函數/固有函數 f

For an LTI system, an input signal x[n] which is an eigenfunction of the system such as x[n] = e^jωn appears at the output of the system with the eigenvalue H(e^jω).