Abstract
Frequently, we need to differentiate quantities like tr(AX) with respect to the elements of X, or quantities like Ax, z′Ax with respect to the elements of (the vectors) x and/or z.
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Notes
- 1.
In fact we dealt with such issues in Chap. 4; the elimination or selection matrix discussed in Remark 4.7, say, S, produces the distinct elements of the symmetric matrix A in the column vector α, by the operation α = Svec(A), while the restoration matrix, also discussed therein, operates on α to produce (restore) vec(A). This is the matrix H defined below, so that H α = vec(A).
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Dhrymes, P.J. (2013). Vector and Matrix Differentiation. In: Mathematics for Econometrics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8145-4_5
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