[선형대수학] 행렬의 거듭제곱 (Power of Matrix)

$\underline{Def}$

Let $A \in M_{n \times n}$.

Define $A^{1}=A,\, A^{2}= A^{1} \cdot A.$

Define recursively that $A^{k}=A^{k-1} \cdot A$  $\forall \geq 2$.

Define $A^{0}=I_{n}$.

 

$\underline{Ex}$

$A=\begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix},\; A^{2}=0$.

Cancellation law does not hold for matrix product.