Appendix03 Matrix Derivative

Types of matrix derivative

Types Scalar Vector Matrix
Scalar
Vector
Matrix

Derivatives with vectors

Vector-by-scalar

Scalar-by-vector

  • application:

Vector-by-vector

Layout conventions

In the case of Vector-by-Vector

Numerator layout

  • layout according to and
  • output size
    • choose as a row Vector.
    • choose as a column Vector.

Denominator layout

  • layout according to and
  • output size
    • choose as a column Vector.
    • choose as a row Vector.

Some Proofs

Numerator Layout

Denominator Layout


Numerator Layout

Denominator Layout

Numerator Layout

Denominator Layout

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