Matrix Norm Calculator
Given an $m\times n$ real or complex matrix $A$, this application calculates five norms of the matrix:
| 1-norm | $\displaystyle\|A\|_{1} = \max_{1\leqslant j\leqslant n} \sum_{i=1}^{m}|a_{ij}|$ |
| infinity-norm | $\displaystyle\|A\|_{\infty} = \max_{1\leqslant i\leqslant m} \sum_{j=1}^{n}|a_{ij}|$ |
| 2-norm | $\displaystyle\|A\|_{2} = \sigma_{max}(A),\quad$ the largest singular value of $A$ |
| F-norm | $\displaystyle\|A\|_{F} = \sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n}|a_{ij}|^2},\quad$ the Frobenius norm of $A$ |
| max-norm | $\displaystyle\|A\|_{max} = \max_{ij}{|a_{ij}|}$ |
See Input Data for the description of how to enter matrix or just click Example for a simple example.