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A question on products of linear combinations of complex matrices

Suppose that $A_1, \dots , A_n, B_1, \dots , B_n \in \Bbb C^{d \times d}$ and that, for every $x \in \mathbb{C}^n$, the following holds $$\left( \sum_i x_i A_i \right) \left( \sum_i x_i A_i \right)^{...
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1 vote
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Injective differential of linear operators on a Hilbertspace

Given a complex Hilbertspace $\mathcal{H}$ of dimension $\dim(\mathcal{H}) = d$ and the set $$\mathcal{F} := \{q\in L(\mathcal{H})\vert\quad \text{rank}(q) = 4 \quad \wedge \lambda^q_{1,2} < 0\ \ \...
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Complex conjugate and unitary complex conjugate

Definition: Let V be complex finite dimensional inner product space Complex Conjugate: $J$ is called complex conjugate on V iff $(i) J$ is antilinear $(ii) J^2 =I$ Definition: Anti-unitary Complex ...
Sushil's user avatar
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