grandes-ecoles 2018 Q33

grandes-ecoles · France · centrale-maths1__pc Invariant lines and eigenvalues and vectors Spectral properties of structured or special matrices
Determine the spectrum of $B$ (the square matrix of order $q$ with coefficient $(i,j)$ equal to 1 if $|i-j|=1$ and 0 otherwise) and a basis of eigenvectors of $B$. 
Determine the spectrum of $B$ (the square matrix of order $q$ with coefficient $(i,j)$ equal to 1 if $|i-j|=1$ and 0 otherwise) and a basis of eigenvectors of $B$.
Paper Questions
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