A new proof is presented for the inequality, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr (XY) ≤ ∥ X ∥₂ · tr Y</tex> . This argument is valid under the condition that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</tex> be real symmetric nonnegative definite; <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> may be any square matrix.
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Saniuk et al. (1987) studied this question.
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