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The Frobenius norm is analogous to the [[dot product]] of Euclidean vectors; square every matrix element and add up the results, then take the positive square root:
:<math>\|\mathbf{A}\| = \sqrt{\mathbf{A}:\mathbf{A}} = \sqrt{\sum_{i=1}^m \sum_{j=1}^n (A_{ij})^2}</math>
It is defined for matrices of any dimension (i.e. no restriction to square matrices).
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