Invert Diagonal Matrix

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Diagonal Matrix Diagonal Matrices

$A \times B = \begin{bmatrix}a_{11}&0&0\\0&a_{22}&0\\0&0&a_{33}\end{bmatrix} \times \begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{bmatrix}$

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$A^{-1} = \begin{bmatrix} A^{-1}_{1}&0&\cdots&0 \\ 0&A^{-1}_{2}&\cdots&0 \\ \vdots&\vdots&\ddots&\vdots \\ 0&0&\cdots&A^{-1}_{q} \end{bmatrix}$

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Diagonal Matrix Diagonal Matrices

$A^{-1} = \frac{\strut 1}{\strut abc}\times \begin{bmatrix}bc & 0 & 0\\0 & ac & 0\\0 & 0 & bc\end{bmatrix}$

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Diagonal matrix

Diagonal Matrix Diagonal Matrices

$A = \begin{bmatrix} a & 0 & 0\\0 & b & 0\\0 & 0 & 0\end{bmatrix}$

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Diagonal Matrix

Diagonal Matrix - Definition, Inverse | Diagonalization

$B^{-1} = \begin{bmatrix}\frac{\strut -1}{\strut 3} & 0 & 0 \\0 & \frac{\strut 1}{\strut 2} & 0 \\ 0 & 0 & \frac{\strut 1}{\strut 5}\end{bmatrix}$

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$A \times B = \begin{bmatrix}-6&0&0\\0&4&0\\0&0&35\end{bmatrix}$

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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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$= \begin{bmatrix}0 & 0 &0\\0 & 0 & 0\\0 & 0 & ab\end{bmatrix}$

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$C \times A = \begin{bmatrix}c_{11}&c_{12}&c_{13}\\c_{21}&c_{22}&c_{23}\\c_{31}&c_{32}&c_{33}\\c_{41}&c_{42}&c_{43}\end{bmatrix}\times \begin{bmatrix}a_{11}&0&0\\0&a_{22}&0\\0&0&a_{33}\end{bmatrix}$

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$A^{-1} = B = \begin{bmatrix} B_{1}&0&\cdots&0 \\ 0&B_{2}&\cdots&0 \\ \vdots&\vdots&\ddots&\vdots \\ 0&0&\cdots&B_{q} \end{bmatrix} = \begin{bmatrix} A^{-1}_{1}&0&\cdots&0 \\ 0&A^{-1}_{2}&\cdots&0 \\ \vdots&\vdots&\ddots&\vdots \\ 0&0&\cdots&A^{-1}_{q} \end{bmatrix}$

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$F_{2\times2} = \begin{bmatrix}4 + 0 & 0 + 0\\0 + 0&0 + 18\end{bmatrix}= \begin{bmatrix}4 & 0\\0 & 18\end{bmatrix}_{2\times2}$

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

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Diagonal Matrix

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$C = \begin{bmatrix}c_{11}&c_{12}&c_{13}\\c_{21}&c_{22}&c_{23}\\c_{31}&c_{32}&c_{33}\\c_{41}&c_{42}&c_{43}\end{bmatrix}$

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Diagonal matrix

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Inverse Matrix

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Inverse Matrix

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Inverse Matrix

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Invert Diagonal Matrix

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