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Results tagged with matrices
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user 74539
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
26
votes
Accepted
Hölder's inequality for matrices
There are (at least two) "generalizations" of Hölder inequality to the non-commutative case. One is the so called tracial matrix Hölder inequality:
$$
|\langle A, B \rangle_{HS} |= |\mathrm{Tr} (A^\da …
- 2,239
1
vote
Regularity for the roots of (characteristic) polynomials with given multiplicity
Edit I have erroneously interpreted the edit. The following only addresses the smoothness of the mapping $x \mapsto (\mathrm{eigenvalues})$.
Given the edit, the assertion is true in a more general …
- 516
1
vote
Is there a simple identity for the derivative of a matrix logarithm w.r.t. a real parameter?
A common definition of the logarithm for (finite dimensional) matrices is via the Dunford-Taylor integral:
$$
\ln(T) := \frac{1}{2\pi i} \oint_\Gamma \ln(z) (z-T)^{-1} dz \, ,
$$
Where $\Gamma$ is a …
- 516