Eigen vectors of a matrix formed by other matrix whose eigen vectors are known.

Asked Oct 08 '20 at 09:37

Active Oct 08 '20 at 14:37

Viewed 108 times

If $B$ has eigenvalues $1, 2, 3$ and $C$ has eigenvalues $4, 5, 6$, and $D$ has eigenvalues $1, 8, 9$, what are the eigenvalues of the $6 x 6$ matrix

$$A = \begin{bmatrix} B & C \\ 0 & D \end{bmatrix}$$

$'0'$ means zero $3 x 3$ matrix

So far I am only able to figure out that the trace of matrix $A$ is $30$ by adding eigen values of $B$ and $C$. Stuck after that can't use the determinant property as we don't know the other values of matrix $A$.

edited Oct 08 '20 at 14:37

Moo

11,311

asked Oct 08 '20 at 09:37

AABHUSHAN REGMI

1

Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Oct 08 '20 at 09:41
@JoséCarlosSantos I hope the problem now meets the standards issued. – AABHUSHAN REGMI Oct 08 '20 at 13:14
https://math.stackexchange.com/questions/207865/the-eigenvalues-of-a-block-matrix This should answer your question – Beyond Infinity Oct 08 '20 at 14:56
@Rishabh Thankyou very much. – AABHUSHAN REGMI Oct 08 '20 at 16:50

Eigen vectors of a matrix formed by other matrix whose eigen vectors are known.

0 Answers0