grandes-ecoles 2013 QI.C.3

grandes-ecoles · France · centrale-maths2__mp Matrices Matrix Decomposition and Factorization
Let $A \in \mathrm{GL}_n(\mathbb{R})$. Determine the matrices $O$ and $S$ when $A = \left(\begin{array}{ccc} 3 & 0 & -1 \\ \sqrt{2}/2 & 3\sqrt{2} & -3\sqrt{2}/2 \\ -\sqrt{2}/2 & 3\sqrt{2} & 3\sqrt{2}/2 \end{array}\right)$. 
Let $A \in \mathrm{GL}_n(\mathbb{R})$. Determine the matrices $O$ and $S$ when $A = \left(\begin{array}{ccc} 3 & 0 & -1 \\ \sqrt{2}/2 & 3\sqrt{2} & -3\sqrt{2}/2 \\ -\sqrt{2}/2 & 3\sqrt{2} & 3\sqrt{2}/2 \end{array}\right)$.
Paper Questions
QI.A.1 QI.A.2 QI.B.1 QI.B.2 QI.B.3 QI.C.1 QI.C.2 QI.C.3 QI.D.1 QI.D.2 QI.D.3 QI.D.4 QI.E QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QIII.A QIII.B QIII.C QIII.D QIV.A QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.C.1 QIV.C.2 QIV.C.3 QIV.C.4 QIV.C.5