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  • 5.4: Diagonalization
    https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/05%3A_Eigenvalues_and_Eigenvectors/5.03%3A_Diagonalization
    This page covers diagonalizability of matrices, explaining that a matrix is diagonalizable if it can be expressed as \(A = CDC^{-1}\) with \(D\) diagonal. It discusses the Diagonalization Theorem, eig...This page covers diagonalizability of matrices, explaining that a matrix is diagonalizable if it can be expressed as \(A = CDC^{-1}\) with \(D\) diagonal. It discusses the Diagonalization Theorem, eigenspaces, eigenvalues, and the significance of linear independence among eigenvectors. Multiple diagonal forms can arise, while geometric and algebraic multiplicities influence diagonalizability.
  • 3.3: Geometry of Diagonalizable Matrices
    https://math.libretexts.org/Courses/Irvine_Valley_College/Math_26%3A_Introduction_to_Linear_Algebra/03%3A_Eigenvalues_and_Eigenvectors/3.03%3A_Geometry_of_Eigenvalues/3.3.01%3A_Geometry_of_Diagonalizable_Matrices
    \[ E_{\frac{1}{2}}=\text{Nul}(A-\frac{1}{2}I)=\text{Nul}\left(\left[\begin{array}{cc}0&-\frac{3}{2}\\0&-\frac{3}{2}\end{array}\right]\right)=\text{Nul}\left( \left[\begin{array}{cc}0&1\\0&0\end{array}...\[ E_{\frac{1}{2}}=\text{Nul}(A-\frac{1}{2}I)=\text{Nul}\left(\left[\begin{array}{cc}0&-\frac{3}{2}\\0&-\frac{3}{2}\end{array}\right]\right)=\text{Nul}\left( \left[\begin{array}{cc}0&1\\0&0\end{array}\right]\right)=\text{Span}\left\{\left[ \begin{array} {c} 1 \\ 0 \end{array} \right]\right\}\nonumber \]

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