The purpose of this work is to carry out a systematic study of a special class of convex functions defined over the space Sₙ of symmetric matrices of order n n. The functions under consideration (Φ: Sₙ R∪ \+∞\) are spectrally defined in the sense that the value Φ(A) depends only on the spectrum \₁(A), …, ₙ(A)\ of the matrix A∈ Sₙ. Fenchel--Legendre conjugation, first- and second-order subdifferentiability, asymptotic behavior, and other concepts of convex analysis are the main ingredients of our exposition.
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Alberto Seeger (1997) studied this question.
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