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Quadratic Form of a Skew-Symmetric Matrix

Medium · Data Science · Quant Trader interview question · linear-algebra, matrix-algebra, skew-symmetric, quadratic-form

You are building a volatility model and need to understand the properties of skew-symmetric matrices. Suppose you have a real skew-symmetric matrix $A$ (meaning $A^T = -A$ ). What is the value of the quadratic form $x^T A x$ for any real vector $x$ ?