access icon free Appendix C: Convenient Formulas for Gradient Operations

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The scalar function trace [ABT] has all the properties of an inner product, so the formulas for differentiation of the trace of various matrix products that appear in reference 1 are of interest for computing the gradients of certain inner products that appear in adaptive array optimization problems. For many problems, the extension of vector and matrix derivative operations to matrix functions of vectors and matrices is important; this generalization is described in reference 2.

Chapter Contents:

  • C.1 References

Inspec keywords: optimisation; matrix algebra; adaptive antenna arrays; gradient methods; differentiation

Other keywords: matrix derivative operations; vector derivative operations; matrix functions; gradient operations; various matrix products; gradients computing; scalar function trace; differentiation; convenient formulas; adaptive array optimization problems; inner product

Subjects: Algebra; Numerical integration and differentiation; Antenna arrays; Optimisation techniques; Other topics in statistics

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