What is the gradient of a scalar function of a symmetric matrix?
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DOI: 10.1007/s13226-022-00313-x
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- Magnus, J.R. & Neudecker, H., 1980. "The elimination matrix : Some lemmas and applications," Other publications TiSEM 0e3315d3-846c-4bc5-928e-f, Tilburg University, School of Economics and Management.
- Friedrich Gebhardt, 1971. "Maximum likelihood solution to factor analysis when some factors are completely specified," Psychometrika, Springer;The Psychometric Society, vol. 36(2), pages 155-163, June.
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Keywords
Matrix calculus; Symmetric matrix; Fréchet derivative; Gradient; Matrix functional;All these keywords.
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