Answer by user63181 for Eigenvectors for shear matrix and diagonalizing.
Look at the second column of the given matrix. The column is $v=(0,1)^T$ and this mean that $Av=v$ so $v$ is an eigenvector associated to the eigenvalue $1$.Since this matrix isn't diagonalizable then...
View ArticleEigenvectors for shear matrix and diagonalizing.
Here is a shear matrix $ \begin{pmatrix} 1 && 0 \\ 2 && 1 \end{pmatrix}$.The eigenvalues are 1. $ \lambda^2 - 2 \lambda + 1 \to \lambda = 1$.So now I try to find the eigenvectors.$...
View ArticleAnswer by C. A. for Eigenvectors for shear matrix and diagonalizing.
If you evaluate this$ \begin{pmatrix} 0 && 0 \\ 2 && 0 \end{pmatrix} \cdot \{x_1, x_2\}=0$You get that $x_1 = 0$ and $x_2$ can be anything. Therefor any vector with $x_1 = 0$ is an...
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