grandes-ecoles 2011 QV.B.2

grandes-ecoles · France · centrale-maths2__psi Matrices Structured Matrix Characterization
We set $\xi_i^j = \begin{cases}0 & \text{if } i = j \\ 1 & \text{otherwise}\end{cases}$ and $N_k = (m_{ij} + k\xi_i^j)$ with $k$ a strictly positive real number.
Express the matrix $N_k$ as a function of the matrices $M, J, I_n$ and the real $k$.
We set $\xi_i^j = \begin{cases}0 & \text{if } i = j \\ 1 & \text{otherwise}\end{cases}$ and $N_k = (m_{ij} + k\xi_i^j)$ with $k$ a strictly positive real number.

Express the matrix $N_k$ as a function of the matrices $M, J, I_n$ and the real $k$.