Matrix Methods in Data Analysis, Signal Processing, and Machine Learning | Mathematics Chapter0:Overview

1. What is Deep learning:

   研究一个function

   这个function干什么映射呢?

   Input data

   Output the meaning of the data

   Function 怎么获得呢?

2. Supporting subjects:

   Optimization: problems of minimizing the error.

   Statistics and probability

3. multiple variables calculus

1. what do you think about mutiply a matrix with a vector?

$Ax=b$;

Case1:既可以看成矩阵A列的向量的线性组合

Case2:看成A的行向量和x的点乘

2. Think about the matrix as a whole thing.

3. Think about all combinations of matrix A.

   All combinations–>a bunch of vectors b–> plot these bunch of vectors.

   Plot: collection: column space of A.a.ka.C(A)

4. what does C(A) looks like?

   $A_{3\times3}$

   $\begin{pmatrix}2&&1&&3\3&&1&&4\5&&7&&12\end{pmatrix}$

5. 我们怎么知道subset是line/space or other thing?

   dimension

6. 矩阵的行rank=列rank

Matrix is the building block of Linear Algebra

Matrix is the building block of DataScience.

7. Rank-1 matrix: $col \times row$=$uv^T$

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