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  • Free bianalytic maps between spectrahedra and spectraballs in a generic setting
    Augat, Meric ...
    Given a tuple ▫$E=(E_1,\dots,E_g)$▫ of ▫$d\times d$▫ matrices, the collection of those tuples of matrices ▫$X=(X_1,\dots,X_g)$▫ (of the same size) such that ▫$\| \sum E_j\otimes X_j\|\le 1$▫ is ... called a spectraball ▫$\mathcal B_E$▫. Likewise, given a tuple ▫$B=(B_1,\dots,B_g)$▫ of $e\times e$ matrices the collection of tuples of matrices ▫$X=(X_1,\dots,X_g)$▫ (of the same size) such that ▫$I + \sum B_j\otimes X_j +\sum B_j^* \otimes X_j^*\succeq 0$▫ is a free spectrahedron ▫$\mathcal D_B$▫. Assuming ▫$E$▫ and ▫$B$▫ are irreducible, plus an additional mild hypothesis, there is a free bianalytic map ▫$p:\mathcal B_E\to \mathcal D_B$▫ normalized by ▫$p(0)=0$▫ and ▫$p'(0)=I$▫ if and only if ▫$\mathcal B_E=\mathcal B_B$▫ and ▫$B$▫ spans an algebra. Moreover ▫$p$▫ is unique, rational and has an elegant algebraic representation.
    Vir: Interpolation and realization theory with applications to control theory : in honor of Joe Ball (Str. 43-60)
    Vrsta gradiva - članek, sestavni del
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 18673497

    Povezava(-e):

    https://doi.org/10.1007/978-3-030-11614-9_2
    DOI

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