Matrix Input
Result
Enter matrix values and click Compute Norms
Compute the Frobenius norm ‖A‖_F, 1-norm (max column sum), ∞-norm (max row sum), and 2-norm (largest singular value / spectral norm). Every formula is computed step by step.
‖A‖_F = √(Σ aᵢⱼ²)
The Frobenius norm treats the matrix as a long vector — easy to compute, great for optimization. The spectral norm (2-norm) measures the worst-case amplification factor of A on any vector and equals its largest singular value.
The 1-norm is the max absolute column sum; the ∞-norm is the max absolute row sum. Both are easy to compute by hand.
"Matrix norms show up everywhere — numerical analysis, machine learning, control theory. Let's connect them to what you're studying."