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6 votes
Accepted

Extension of scalars for bounded chain complexes of $kG$-modules

Since $k'$ is finite dimensional over $k$, you can move it from inside to outside a Hom in the last isomorphism below. $$\operatorname{\rm Hom}_{k'G}(k'\otimes_k C,k'\otimes_k D)\cong \operatorname{\...
Dave Benson's user avatar
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3 votes

What is the "natural" or "physical" norm on the Hessian matrix (and other higher derivatives)?

We would like a matrix norm $\|\cdot\|$ to be invariant under orthogonal transformations in the sense that $\|A\|=\|UAV\|$ whenever $U,V$ are orthogonal mappings. But by the singular value ...
Joseph Van Name's user avatar
2 votes
Accepted

Where does $V$ from the spectral decomposition $A = VDV^*$ lie, if $A$ has only imaginary entries?

The $n\times n$ imaginary matrix $A$ satisfies $A^\top=-A$, so it is skew-symmetric. The Youla decomposition is $$A=iO\Sigma O^\top,$$ where $O$ is a real orthogonal matrix and $\Sigma$ is a real ...
Carlo Beenakker's user avatar

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