Block Diagonalize

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Solved Problem 4: If A = SAS-1, diagonalize the block matrix | Chegg.com

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$A = \begin{bmatrix} A_{1}&0&\cdots&0 \\ 0&A_{2}&\cdots&0 \\ \vdots&\vdots&\ddots&\vdots \\ 0&0&\cdots&A_{r} \end{bmatrix}$

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$A = \begin{bmatrix} A_{11}&A_{12}&\cdots&A_{1r} \\ A_{21}&A_{22}&\cdots&A_{2r} \\ \vdots&\vdots&\ddots&\vdots \\ A_{r1}&A_{r2}&\cdots&A_{rr} \end{bmatrix} \qquad A_{\alpha \beta} = 0 \text{ if } \alpha \ne \beta$

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$B = \begin{bmatrix} B_{11}&B_{12}&\cdots&B_{1q} \\ B_{21}&B_{22}&\cdots&B_{2q} \\ \vdots&\vdots&\ddots&\vdots \\ B_{q1}&B_{q2}&\cdots&B_{qq} \end{bmatrix} \qquad I = \begin{bmatrix} I_{11}&I_{12}&\cdots&I_{1q} \\ I_{21}&I_{22}&\cdots&I_{2q} \\ \vdots&\vdots&\ddots&\vdots \\ I_{q1}&I_{q2}&\cdots&I_{qq} \end{bmatrix}$

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$C = \begin{bmatrix} C_{1}&0&\cdots&0 \\ 0&C_{2}&\cdots&0 \\ \vdots&\vdots&\ddots&\vdots \\ 0&0&\cdots&C_{q} \end{bmatrix}$

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Block Diagonalize

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