1. Derivative of scalar forms

2. Derivative of matrix forms

3. Derivative of vector products of the form:

4. Useful properties of the trace operator

5. Derivative of vector and matrix products of the form:
square matrix
scalar

6. Matrix inversion lemma
Inverse
Matrix inversion lemma
If the appropriate inverses exist:

7. Eigen decomposition of a square matrix
Assume we have a square matrix A with eigen values:
And corresponding eigen vectors:

8. Eigen decomposition of a square matrix, continued
Diagonal matrix with eigen values of A
Matrix of eigen vectors of A

9. Eigen decomposition of a symmetric matrix
For symmetric matrices, eigen vectors for distinct eigen values are orthogonal.
All eigen values of a real symmetric matrix are real.
All eigen values of a positive semi-definite matrix are non-negative:
Diagonal matrix with eigen values of A
Matrix of normalized eigen vectors of A

10. Some useful properties of determinant of square matrices
(nxn)
eigen values of A

11. Derivative of determinant forms