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Frobenius vs Spectral Norm

Medium · Linear Algebra & Machine Learning · Quant Trader interview question · linear-algebra, matrix-norms, frobenius-norm, spectral-norm

Let $A$ be a real-valued $m imes n$ matrix. The Frobenius norm of $A$, denoted $||A||_F$, is defined as the square root of the sum of the squares of its elements. The spectral norm of $A$, denoted $||A||_2$, is defined as the largest singular value of $A$. Which of the following statements is always true for any real-valued $m imes n$ matrix $A$?

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