# Tagged Questions

58 views

### Recurrence - using power series

Could you help me in solving this recursion( a closed form ) using power series $\mu(n)=\mu(nā1)k_0+(nā1)\mu(nā2) k_1 \tag 1$, where $k_0,k_1$ are constants $\mu(0)=3,\mu(1)=5$ HINT: We can think ...
357 views

### Converting recursive equations into matrices

How do we convert recursive equations into matrix forms? For instance, consider this recursive equation(Fibonacci Series): $$F_n = F_{n-1} + F_{n-2}$$ And it comes out to be that the following that ...
104 views

63 views

203 views

### Matrix recurrence equation

We define a $"2 \times 2"$matrix $A$. The following recurrence equation is given:$$A^{k+1}=\frac{A^k}{k}+I,(k=1,N)$$where $I$ is the identity matrix. How can I find the matrix $A$? Thanks
601 views

### Recurrence for a lagged Fibonacci sequence

I know how to do the matrix for the standard $f(n) = f(n-1) + f(n-2)$ relationship, but what if it's piecewise? For instance, $f(1)$ through $f(30)$ have some preset values, and then for $f(31)$ ...
For a matrix $A\in\mathbb{K}^{n\times n}$ where $\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}$ the characteristic polynomial is defined as \chi_A(\lambda) := \text{det}(A-\lambda I_n) = \sum_{k=0}^n c_k ...