Oblicz normę pierwsza, \(\displaystyle{ \infty}\) i Frobeniusa macierzy:
a) \(\displaystyle{ \left[\begin{array}{ccc}3&i&-i\\2&5&2+3\\2-i&1&3\end{array}\right]}\)
b)\(\displaystyle{ \left[\begin{array}{ccc}1&2&-1\\1&2&1\\2&2&1\end{array}\right]}\)
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Normy macierzowe
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michal422
Normy macierzowe
nie wiem czy dobrze:
b)
\(\displaystyle{ \left[\begin{array}{ccc}1&2&-1\\1&2&1\\2&2&1\end{array}\right]}\)
czyli \(\displaystyle{ \left| \left| A\right| \right| _{ \infty }=5}\)?
dla \(\displaystyle{ \left| \left| A\right| \right| _{1}}\)
\(\displaystyle{ max\left\{ 4,6,3\right\}}\) czyli \(\displaystyle{ \left| \left| A\right| \right| _{1} =6}\)
a)
\(\displaystyle{ \left[\begin{array}{ccc}3&i&-i\\2&5&2+3\\2-i&1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}5\\12\\ \sqrt{5}+4 \end{array}\right]}\)
czyli \(\displaystyle{ \left| \left| A\right| \right| _{ \infty }=12}\)?
dla \(\displaystyle{ \left| \left| A\right| \right| _{1}}\)
\(\displaystyle{ max\left\{ \sqrt{5}+5 ,7,9\right\}}\) czyli \(\displaystyle{ \left| \left| A\right| \right| _{1} =9}\)
b)
\(\displaystyle{ \left[\begin{array}{ccc}1&2&-1\\1&2&1\\2&2&1\end{array}\right]}\)
czyli \(\displaystyle{ \left| \left| A\right| \right| _{ \infty }=5}\)?
dla \(\displaystyle{ \left| \left| A\right| \right| _{1}}\)
\(\displaystyle{ max\left\{ 4,6,3\right\}}\) czyli \(\displaystyle{ \left| \left| A\right| \right| _{1} =6}\)
a)
\(\displaystyle{ \left[\begin{array}{ccc}3&i&-i\\2&5&2+3\\2-i&1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}5\\12\\ \sqrt{5}+4 \end{array}\right]}\)
czyli \(\displaystyle{ \left| \left| A\right| \right| _{ \infty }=12}\)?
dla \(\displaystyle{ \left| \left| A\right| \right| _{1}}\)
\(\displaystyle{ max\left\{ \sqrt{5}+5 ,7,9\right\}}\) czyli \(\displaystyle{ \left| \left| A\right| \right| _{1} =9}\)