grandes-ecoles 2025 Q19

grandes-ecoles · France · mines-ponts-maths2__mp Matrices Linear Transformation and Endomorphism Properties
Show, using questions 9 and 13, that if $p$ has no stable root and if $J(p)$ is not invertible then there exists a non-zero polynomial $q$ with real coefficients of degree at most $n-1$ such that $q(S^\top) U = 0_{n,1}$.
Show, using questions 9 and 13, that if $p$ has no stable root and if $J(p)$ is not invertible then there exists a non-zero polynomial $q$ with real coefficients of degree at most $n-1$ such that $q(S^\top) U = 0_{n,1}$.