Frobenius dot product is achieved by computing the hadamard multiplication (elementwise) of two matrices <A,B>with the same dimensionality and summing up all the elements.
Another way to achieve the Frobenius dot product is to vectorise(build columnwise: vec(A),vec(B)) both matrices to two vectors with the same size and then perform a dot product between them.
Another way to achieve Frobenius dot product is the to take the trace of the dot product of the first matrix with the second.
<A,B>F = trace(sum(Transpose(A)B)).
Another thing that derives from the forbinus dot product is a way to calculate the magnitude(norm) of a matrix which is:
The square root of trace on the matrix dot product with itself.
norm(A) = √<A,A>F = √trace(sum(Transpose(A)*A))
