0
votes
2answers
92 views

How do I write this matrix in Jordan-Normal Form

I have the matrix $A=\begin{pmatrix}2&2&1\\-1&0&1\\4&1&-1\end{pmatrix}$, I want to write it in Jordan-Normal Form. I have $x_1=3,x_2=x_3=-1$ and calculated eigenvectors ...
1
vote
1answer
69 views

Is eigenvectors/eigenvalues of symetric matrix related with eigenvectors/eigenvalues of its block?

$A$ is square symmetric matrix as: $$A=\begin{pmatrix} A_1&A_2 \\ A_3 & A_4 \end{pmatrix}$$ I have two points which need help to understand clearly: All blocks $A_1$, $A_2$, $A_3$, $A_4$ ...
0
votes
1answer
65 views

bilinear equation OR diagonal matrix search

Having a real square $n \times n$ symmetric matrix $B$ (which consists of 2 square blocks of positive numbers and 2 rectangular blocks of negative numbers) I want a real diagonal matrix $D$ such that ...