Vector and Matrix Differentiation Principles
Explore the concepts of vector and matrix differentiation, including partial derivatives, symmetric matrices, Jacobi matrix, and Hessian matrix. Understand the first and second derivatives of functions with respect to vectors.
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Presentation Transcript
LECTURE SEVEN Differentiation with Vectors and Matrices
The vector of partial derivatives is: If f(x) is constant for all x ; then:
If f(x) = x'Ax ; (A is symmetric) ; then: If ( A is not symmetric A A') ; then: If f(x) = x'Ax ; (A is identity) ; then:
JACOBI MATRIX It represents the first derivative of some function with respect to x vector.
HESSIAN MATRIX It represents the second derivative of some function with respect respectively. to x' and x vectors
