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numerical-range:generalizations:q-numerical-range

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numerical-range:generalizations:q-numerical-range [2019/06/11 14:31]
plewandowska [q--numerical range]
numerical-range:generalizations:q-numerical-range [2019/06/11 14:31] (current)
plewandowska [Definition]
Line 5: Line 5:
 Let $A$ be an $d \times d$ matrix. The q-numerical range of $A$ is the set: Let $A$ be an $d \times d$ matrix. The q-numerical range of $A$ is the set:
 \[ \[
-W_q(A) = \left\{ z \in \mathbb{C}: z = \bra{x}A\ket{y}, ​|\braket{x}{y}= q, \ket{x} \in \mathbb{C}^d,​ \ket{y} \in \mathbb{C}^d,​ \braket{x}{x} = 1, \braket{y}{y} = 1 \right\}.+W_q(A) = \left\{ z \in \mathbb{C}: z = \bra{x}A\ket{y},​ \braket{x}{y} = q, \ket{x} \in \mathbb{C}^d,​ \ket{y} \in \mathbb{C}^d,​ \braket{x}{x} = 1, \braket{y}{y} = 1 \right\}.
 \] \]
  
numerical-range/generalizations/q-numerical-range.txt · Last modified: 2019/06/11 14:31 by plewandowska