grandes-ecoles 2014 QI.B.1

grandes-ecoles · France · centrale-maths2__psi Matrices Matrix Algebra and Product Properties
Let $A$ and $B$ be two matrices of $\mathcal { M } _ { n } ( \mathbb { R } )$. Show that if, for all $X$ and $Y$ of $\mathbb { R } ^ { n } , { } ^ { t } X A Y = { } ^ { t } X B Y$ then $A = B$. 
Let $A$ and $B$ be two matrices of $\mathcal { M } _ { n } ( \mathbb { R } )$. Show that if, for all $X$ and $Y$ of $\mathbb { R } ^ { n } , { } ^ { t } X A Y = { } ^ { t } X B Y$ then $A = B$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B QII.C QII.D QIII.A QIII.B QIII.C QIII.D QIII.E.1 QIII.E.2 QIII.F.1 QIII.F.2 QIII.F.3 QIII.F.4 QIII.G QIII.H QIII.I