Complex Vector Representation from Paired Real Components
A -dimensional real vector can be reinterpreted as a -dimensional complex vector . This transformation is achieved by pairing consecutive real components to form the real and imaginary parts of new complex components. The resulting vector is expressed as a sequence of its components according to the formula: where represents the imaginary unit.
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Ch.2 Generative Models - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
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Complex Vector Representation from Paired Real Components
A vector
vis defined as havingd/2dimensions. If the parameterdis equal to 12, which of the following shows the correct component-wise representation of the vectorv?A vector
vis represented in component-wise notation asv = (v_1, v_2, v_3, v_4, v_5). If this vector is described as beingd/2-dimensional, the value ofdmust be ____.Verifying Input Vector Dimensions
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A 6-dimensional real vector is given by . If this vector is reinterpreted as a 3-dimensional complex vector by pairing consecutive components (where the first component of a pair is the real part and the second is the imaginary part), what is the resulting complex vector?
Reconstructing a Real Vector from its Complex Representation
A 7-dimensional real vector can be reinterpreted as a 3.5-dimensional complex vector by pairing its consecutive real components to form the real and imaginary parts of new complex components.