Least Squares Estimation, Matrix Derivation (Normal Equation)

1. Matrix derivation:

            

    The independent variable of the function is a matrix, and the derivation is to separate each element of the matrix to form a new matrix.

    example:

            

2. The trace of the matrix:

            

    Common properties of matrix traces:

            

    Matrix trace and matrix derivation related conclusions:

            

            

3. Prove the normal equation of least squares (matrix derivation method):