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Rodrigo de Azevedo
Rodrigo de Azevedo
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Reference request: Relation between the eigenvalues of a block matrix and the eigenvalues of its diagonal blocks

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Rodrigo de Azevedo
Rodrigo de Azevedo
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Consider the block matrix $M = \begin{bmatrix} A & B \\ C & D \end{bmatrix}$ of order $(m+n) \times (m+n)$. I block matrix

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

I need references where they are talking about the relation between the eigenvalues of $M$ and the eigenvalues of $A$ and $D$. I want to learn under what circumstances such a relation exists. The simplest of such a possibility is $B=0$ or $C=0$. I believe there are other non-trivial cases. Kindly share some references. Thank you.

Consider the block matrix $M = \begin{bmatrix} A & B \\ C & D \end{bmatrix}$ of order $(m+n) \times (m+n)$. I need references where they are talking about the relation between the eigenvalues of $M$ and the eigenvalues of $A$ and $D$. I want to learn under what circumstances such a relation exists. The simplest of such a possibility is $B=0$ or $C=0$. I believe there are other non-trivial cases. Kindly share some references. Thank you.

Consider the $(m+n) \times (m+n)$ block matrix

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

I need references where they are talking about the relation between the eigenvalues of $M$ and the eigenvalues of $A$ and $D$. I want to learn under what circumstances such a relation exists. The simplest of such a possibility is $B=0$ or $C=0$. I believe there are other non-trivial cases. Kindly share some references. Thank you.

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GA316
GA316
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Reference request: Relation between eigenvalues of a block matrix and the eigenvalues of its diagonal blocks

Consider the block matrix $M = \begin{bmatrix} A & B \\ C & D \end{bmatrix}$ of order $(m+n) \times (m+n)$. I need references where they are talking about the relation between the eigenvalues of $M$ and the eigenvalues of $A$ and $D$. I want to learn under what circumstances such a relation exists. The simplest of such a possibility is $B=0$ or $C=0$. I believe there are other non-trivial cases. Kindly share some references. Thank you.