3
votes
1answer
27 views

Find the polynomial function

Anybody knows how to find the polynomial function with evaluated values, where if the degree is $n$ I have $n+1$ values of the function like $f(0) = a_0, f(1) = a_1, \ldots, f(n) = a_n$.
0
votes
0answers
30 views

Converting sums to matrix equations

I am able to transform basic sums to vector/matrix equations. But now I have something like: $$ c_{p,q} = \sum_{n=1}^N \sum_{r=1}^R \sum_{s=1}^S e_n x_{n-q-s,p} \cdot h_{r,s} \cdot g_r \cdot ...
1
vote
0answers
45 views

Solving the equation $AX+XA' = 0$

I am trying to solve the equation $AX + XA' = 0$ I could find how to solve when "$+$" is a "$-$" or $X$ is conjugated instead of $A$. Is there a solution for this problem too? In particular, I am ...
2
votes
1answer
56 views

Method of characteristics for a system of pdes

I can do parts a) and b) as follows $\begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1\end{pmatrix}\frac{\partial}{\partial{}x}\begin{pmatrix} u \\ v \\ w\end{pmatrix}+\begin{pmatrix} ...
0
votes
1answer
31 views

Can someone please provide an intuition behind cramer's rule?

See question. I usually get concepts like this very quickly (no studying required), but this one looks like Chinese. Can someone please help me understand a brief intuition behind Cramer's rule for ...
2
votes
2answers
72 views

Simplfy a complex matrix into a real one

I encounter systems of linear complex equations (At most 3 equations) in my circuit analysis course. The calculator I am using is Casio fx-991ES and it only accepts real elements when in matrix or ...
0
votes
0answers
25 views

Is there a non-zero solution to this system of equations?

I have a system of equations. $\mu_1p_1=(1-p_1)\sum_{i=1, i\ne 1}^N \lambda_{i1}p_i$ $\mu_2p_2=(1-p_2)\sum_{i=1, i\ne 2}^N \lambda_{i2}p_i$ and so on. The values $\mu_k$ and $\lambda_{kl}$ are ...
0
votes
0answers
107 views

Matrix equation existence of solutions

In my textbook (Linear Algebra and its applications by David C. Lay) one finds the following theorem: Let A be an $m\times n$ matrix. Then the following statements are logically equivalent: ...