Tagged Questions
0
votes
1answer
24 views
k-fold matrix product
For $k \in \mathbb{N}$, $B,C \in \mathbb{R^{n,n}}$, given the matrices $B,C$ , calculate all powers $B^k$ and
$C^k$
I'm a bit puzzled by this task. I assume it's supposed to practice handling ...
4
votes
4answers
75 views
Can you raise a Matrix to a non integer number? [duplicate]
So I heard you can take a matrix A to the power 2, take it to a -3th power and multiply it by an irrational number. You can also do some other non-intuitive things like taking e to the power of a ...
1
vote
2answers
83 views
Trace of the matrix power
Say I have matrix $A = \begin{bmatrix}
a & 0 & -c\\
0 & b & 0\\
-c & 0 & a
\end{bmatrix}$.
What is matrix trace
tr(A^200)
Thanks much!
3
votes
2answers
111 views
Why does the $n$-th power of a Jordan matrix involve the binomial coefficient?
I've searched a lot for a simple explanation of this. Given a Jordan block $J_k(\lambda)$, its $n$-th power is:
$$
J_k(\lambda)^n = \begin{bmatrix}
\lambda^n & \binom{n}{1}\lambda^{n-1} & ...
0
votes
0answers
17 views
Large powers of a banded and of a Toeplitz matrix
I would like to compute the p-th power of A, where A is a banded matrix. What is the best method to do that, if we suppose that p is large? In another case, where A is a Toeplitz matrix, which method ...
6
votes
1answer
136 views
Power of a block matrix with eigenvalues on the unit circle
In the expression
$$\begin{bmatrix}A & C \\ 0 & B\end{bmatrix}^n = \begin{bmatrix}A^n & * \\ 0 & B^n\end{bmatrix},$$
I wonder whether the term denoted by * can be expressed in a simple ...
