Equivalence of 2D Vector Rotation Representations
A 2-dimensional vector can be rotated by an angle θ using two different mathematical approaches. The first approach involves multiplying the vector [x₁, x₂] by a standard 2x2 rotation matrix. The second approach treats the vector as a complex number z = x₁ + i·x₂ and multiplies it by e^(iθ).
Demonstrate mathematically that these two approaches are equivalent by showing that the components of the resulting vector from the matrix multiplication are identical to the real and imaginary parts of the resulting complex number.
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Ch.3 Prompting - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
Analysis in Bloom's Taxonomy
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