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Frobenius Norm §

• Scientific Computing - Lecture 3 - Frobenius Norm

Frobenius Norm Definition §

Consider the Frobenius inner product (or dot product) between two matrices:

This product induces the Frobenius Norm as:

Frobenius Norm Trace Notation §

In proof is often used the Trace Notation:

• the matrix product is a matrix whose diagonal entries are sums of products of corresponding rows of and columns of
• The trace is the sum of the diagonal entries

Example:

Applying directly the frobenius product we obtain:

Using trace:

The sum of the diagonal entries is 70:

So the result is the same