Answer by user145318 for Diagonalization problems (eigenvalues and vectors)
If you have an eigenvalue with multiplicity n, then you must have n linearly independent eigenvectors from that eigenvalue in order for the matrix to be diagonalizable.
View ArticleAnswer by Amzoti for Diagonalization problems (eigenvalues and vectors)
Hints:The first is not diagonalizable, but we can use the Jordan Normal Form. We get:$$A = PJP^{-1} =\left(\begin{array}{cc} 1 & -1 \\ 1 & 0 \\\end{array}\right) \left(\begin{array}{cc} 1 &...
View ArticleDiagonalization problems (eigenvalues and vectors)
I am trying to diagonalize the following matrices:$$A = \begin{pmatrix}0 & 1\\-1 & 2\end{pmatrix}\qquad B = \begin{pmatrix}1 & 2\\-1&-1\end{pmatrix}$$For matrix $A$, I find an...
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