Macierz rzutu ortogonalnego

dam1ann · Post autor: **dam1ann** » 9 maja 2016, o 16:00

Wyznaczyć macierz rzutu ortogonalnego na kierunek wektora \(\displaystyle{ u}\).
\(\displaystyle{ u=\left( \frac{1}{3},\frac{2}{3},-\frac{2}{3}\right)}\)

andkom · Post autor: **andkom** » 10 maja 2016, o 07:50

\(\displaystyle{ \frac1{\|u\|^2}\cdot u^T\cdot u=\frac1{\left(\frac13\right)^2+\left(\frac23\right)^2+\left(-\frac23\right)^2}\cdot\begin{pmatrix}\frac13\\\frac23\\-\frac23\end{pmatrix}\cdot\left(\frac13,\frac23,-\frac23\right)=\begin{pmatrix}\frac19&\frac29&-\frac29\\\frac29&\frac49&-\frac49\\-\frac29&-\frac49&\frac49\end{pmatrix}}\)