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- matrices - What is the difference between the Frobenius norm and the 2 . . .
The Frobenius norm is always at least as large as the spectral radius The Frobenius norm is at most $\sqrt{r}$ as much as the spectral radius, and this is probably tight (see the section on equivalence of norms in Wikipedia) Note that the Schatten $2$-norm is equal to the Frobenius norm
- How to prove that the Frobenius endomorphism is surjective?
The Frobenius homomorphism is often called the Frobenius endomorphism, since "endomorphism" is a more specific term meaning "map from something to itself" However, I'll use "homomorphism" here to avoid confusion
- number theory - Frobenius elements - Mathematics Stack Exchange
The following is standard in any algebraic number theory textbook Frobenius elements are first defined for finite fields
- Frobenius Inequality Rank - Mathematics Stack Exchange
Frobenius Inequality Rank Ask Question Asked 11 years, 9 months ago Modified 7 months ago Viewed 10k
- Solving ODEs: The Frobenius Method, worked examples
The wikipedia article begins by saying that the Frobenius method is a way to find solutions for ODEs of the form $ x^2y'' + xP(x) + Q(x)y = 0 $ To put (1) into that form I might multiply across by x, giving me
- linear algebra - Relation between Frobenius norm and trace . . .
$\begingroup$ (For motivation, we can drop this assumption if we replace $\lambda_{max}(P)$ with $\|P\|_F$; the bound then follows from Cauchy-Schwarz and the fact that the Frobenius norm is submultiplicative But the Frobenius norm bounds the spectral radius from above, so this bound is weaker than the desired one ) $\endgroup$ –
- When is the Frobenius endomorphism an automorphism?
I figured out that this map is called the Frobenius endomorphism, and that it can be a hint, if we show that any non-zero field homomorphism to itself is automatically an automorphism, but I don't know why it has to work
- linear algebra - How to express the Frobenius norm of a matrix as the . . .
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