Linear Algebra Quiz
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MATRIX DECOMPOSITIONS & STRUCTURE
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Consider the symmetric matrix A=(210121012)A = \begin{pmatrix} 2 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 1 & 2 \end{pmatrix}. During the orthogonal diagonalization process, it is found that one eigenvalue is λ=2\lambda = 2 with geometric multiplicity 1. If PP is the orthogonal matrix that diagonalizes AA, which statement about the structure of PTAPP^TAP is necessarily true?
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