Frobenius Norm.

• It is called Frobenius norm (Frobenius norm) or Hilbert-Schmidt norm. (Hilbert-Schmidt norm) (the latter is usually used exclusively for operators in Hilbert spaces). Although this norm has several different definitions,

$\Vert A{\Vert }_F=\sqrt{{\sum }_{i=1}^m{\sum }_{j=1}^n|a_{ij}{|}^2}=\sqrt{\mathrm{tr}(A^{\ast }A)}=\sqrt{{\sum }_{i=1}^{\min \{m,n\}}{\sigma }_i^2}$ The following can be written as follows. where A∗ denotes adjoint of matrix A, σi denotes singular value of matrix A, and tr denotes trace of matrix A. [matrix norm - Wikipedia https://ja.wikipedia.org/wiki/%E8%A1%8C%E5%88%97%E3%83%8E%E3%83%AB%E3%83%A0#%E3%83%95%E3%83%AD%E3%83%99%E3%83%8B%E 3%82%A6%E3%82%B9%E3%83%BB%E3%83%8E%E3%83%AB%E3%83%A0]Matrix norm

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