The scalar function trace [AB^T] 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: matrix algebra; optimisation; adaptive antenna arrays; differentiation; gradient methods

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

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