Apr 21, 2016 · Yes. Assuming that your matrix is in fact diagonalizable (which will happen if all of the eigenvalues are distinct, but can also sometimes happen when you have repeated …

Jun 23, 2019 · Calculating Eigenvectors of a Diagonal Matrix Ask Question Asked 6 years, 4 months ago Modified 1 year, 11 months ago

Aug 29, 2015 · The relationship between diagonal entries and eigenvalues of a diagonalizable matrix Ask Question Asked 10 years, 2 months ago Modified 10 years, 2 months ago

You have a $4n \times 4n$ matrix, so you expect $4n$ eigenvalues (with multiplicities accounted separately). The eigenvalues will be indeed the eigenvalues of the original submatrices.

Proof that Eigenvalues are the Diagonal Entries of the Upper-Triangular Matrix in Axler Ask Question Asked 12 years, 10 months ago Modified 1 year, 5 months ago

For another approach for a proof you can use the Gershgorin disc theorem (sometimes Hirschhorn due to pronounciation differences between alphabets) to prove the disks for the …

May 18, 2015 · 2 If the eigenvalues are say $-1$, $-1$ and $2$ for a $3$ x $3$ matrix, then when comes to the diagonal matrix, is it (from top left, to bottom right) $-1$ $-1$ $2$ or $2$ $-1$ $ …

Dec 26, 2018 · 20 I doubt there is an analytic expression for all but the smallest matrix dimensions. However, there is an inexpensive way to compute the eigenvalues of rank-one …

But for $\theta = \pi/2$, the product has eigenvalues $8 = 2 \cdot 4$ and $3 = 1 \cdot 3$, the "middle" two products of the eigenvalues of the two original matrices. For intermediate values …

May 15, 2017 · As the other posters comment, there are diagonal matrices which are not multiples of the identity, for example $$ \begin {bmatrix}1&0\\0&2\end {bmatrix} $$ and if all the …