Norm

Choosing Norm from the Matrices submenu gives the 2-norm of a vector or matrix. The 2-norm of a vector is the Euclidean length of the vector.

$\displaystyle \left\Vert\vphantom{
\begin{array}{c}
a \\
b
\end{array}
}\right.$$\displaystyle \begin{array}{c}
a \\
b
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{c}
a \\
b
\end{array}
}\right\Vert$ =  $\displaystyle \sqrt{{a^{2}+b^{2}}}$                $\displaystyle \left\Vert\vphantom{
\begin{array}{c}
a \\
b \\
c \\
d
\end{array}
}\right.$$\displaystyle \begin{array}{c}
a \\
b \\
c \\
d
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{c}
a \\
b \\
c \\
d
\end{array}
}\right\Vert$ =  $\displaystyle \sqrt{{a^{2}+b^{2}+c^{2}+d^{2}}}$

The 2-norm of a matrix A is its largest singular value—the number defined by

$\displaystyle \left\Vert\vphantom{ A}\right.$A$\displaystyle \left.\vphantom{ A}\right\Vert$ = $\displaystyle \max_{{x\neq 0}}^{}$$\displaystyle {\frac{{\left\Vert Ax\right\Vert }}{{\left\Vert
x\right\Vert }}}$

$\blacktriangleright$ Matrices + Norm

$\left(\vphantom{
\begin{array}{cc}
2 & 3 \\
5 & 7
\end{array}
}\right.$$\begin{array}{cc}
2 & 3 \\
5 & 7
\end{array}$$\left.\vphantom{
\begin{array}{cc}
2 & 3 \\
5 & 7
\end{array}
}\right)$, 2-norm: ${\frac{{1}}{{2}}}$$\sqrt{{89}}$ + ${\frac{{1}}{{2}}}$$\sqrt{{85}}$ 8pt        

$\left(\vphantom{
\begin{array}{rrr}
2 & -1 & 0 \\
-1 & 2 & -1 \\
0 & -1 & 2
\end{array}
}\right.$$\begin{array}{rrr}
2 & -1 & 0 \\
-1 & 2 & -1 \\
0 & -1 & 2
\end{array}$$\left.\vphantom{
\begin{array}{rrr}
2 & -1 & 0 \\
-1 & 2 & -1 \\
0 & -1 & 2
\end{array}
}\right)$, 2-norm: 2 + $\sqrt{{2}}$

You obtain a numerical approximation if at least one entry is in floating-point form.

$\blacktriangleright$ Matrices + Norm

$\left(\vphantom{
\begin{array}{cc}
.2 & .3 \\
.5 & .7
\end{array}
}\right.$$\begin{array}{cc}
.2 & .3 \\
.5 & .7
\end{array}$$\left.\vphantom{
\begin{array}{cc}
.2 & .3 \\
.5 & .7
\end{array}
}\right)$, 2-norm: .93268

The 2-norm of a matrix can also be obtained with double brackets.

$\blacktriangleright$ To put norm symbols around a matrix

1.
Select the matrix by using the mouse or by pressing SHIFT + RIGHT ARROW.

2.
ClickitbpF0.3009in0.3009in0.0701infences.wmfor choose Insert + Brackets. Select the norm symbols. Choose Ok.