Mathematical foundations of machine learning (2) - Linear Algebra

Linear Algebra

Matrix operations:

1. Addition: adding para
2. Multiplication: Each multiplied by
3. Matrix Multiplication
4. Only the square inverse matrix

Matrix guide

${\frac{\partial Ax}{\partial x}=A^T}$
seek derivative is transposed coefficient matrix after

Jacobian matrix and Hessian matrix

Writing rules:

1. A Jacobian matrix :( partial derivative matrix)
   behavior: each function $f_i$Changes
   as: each variable $x_j$The change
2. Hessian matrix of second order partial derivative matrix :()
   Behavior: The first change factor for each partial derivative function $x_i$
   As: The second change factor for each partial derivative function $x_j$

vector

Operations: multiplication, addition, subtraction, and the inner product
projected
correlation
spatial dimension and group

The main application

PCA, SVD theories