$$\Vert v\Vert ＝\sqrt{{\displaystyle \underset{k＝1}{\overset{N}{\sum }}{\left|v_k\right|}^2}}．$$

$${\Vert v\Vert }_p＝{［{\displaystyle \underset{k＝1}{\overset{N}{\sum }}{\left|v_k\right|}^p}]}^{1/p}，$$

$${\Vert X\Vert }_1＝\underset{1\le j\le n}{\mathrm{马克斯}}（{\displaystyle \underset{我＝1}{\overset{米}{\sum }}\left|{\mathrm{一个}}_{我j}\right|}）．$$

$${\Vert X\Vert }_{\infty }＝\underset{1\le 我\le 米}{\mathrm{马克斯}}（{\displaystyle \underset{j＝1}{\overset{n}{\sum }}\left|{\mathrm{一个}}_{我j}\right|}）．$$

$${\Vert X\Vert }_F＝\sqrt{{\displaystyle \underset{我＝1}{\overset{米}{\sum }}{\displaystyle \underset{j＝1}{\overset{n}{\sum }}{\left|{\mathrm{一个}}_{我j}\right|}^2}}}＝\sqrt{\text{跟踪}（X^{\_\_}X）}．$$