grandes-ecoles 2012 QIII.B.4

grandes-ecoles · France · centrale-maths2__mp Matrices Matrix Norm, Convergence, and Inequality
Throughout this part, $n$ denotes an integer greater than or equal to 3, and $p = [(n+1)/2]$ is the integer part of $(n+1)/2$.
Verify that if $n = 3$, condition III.1 is equivalent to: $2(\lambda_1^2 + \lambda_2^2 + \lambda_3^2) \geqslant 3(\lambda_1\lambda_2 + \lambda_1\lambda_3 + \lambda_2\lambda_3)$. 
Throughout this part, $n$ denotes an integer greater than or equal to 3, and $p = [(n+1)/2]$ is the integer part of $(n+1)/2$.

Verify that if $n = 3$, condition III.1 is equivalent to: $2(\lambda_1^2 + \lambda_2^2 + \lambda_3^2) \geqslant 3(\lambda_1\lambda_2 + \lambda_1\lambda_3 + \lambda_2\lambda_3)$.
Paper Questions
QI.A QI.B.1 QI.B.2 QI.C.1 QI.C.2 QI.C.3 QI.D QII.A.1 QII.A.2 QII.B.1 QII.B.2 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QIII.A.1 QIII.A.2 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.C.1 QIII.C.2 QIII.D.1 QIII.D.2 QIII.D.3