Math Problem Statement

If x = (2, 1 + i, i) and y = (2 - i, 2, 1 + 2i) then verify Schwarz's inequality

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Complex Numbers
Vector Spaces

Formulas

Cauchy-Schwarz inequality: |⟨x, y⟩|^2 ≤ ⟨x, x⟩⟨y, y⟩
Inner product: ⟨x, y⟩ = Σ x_k * conj(y_k)
Magnitude of a complex number: |a + bi| = sqrt(a^2 + b^2)

Theorems

Cauchy-Schwarz Inequality

Suitable Grade Level

Undergraduate Level (Math/Physics)