Machine learning [] [] of linear algebra matrix derivation

Reprinted Source: https://blog.csdn.net/u010976453/article/details/54381248

table of Contents

1, X is a scalar

1.1 Y scalar scalar derivative X

1.2 Y scalar vector derivation X

Scalar matrix Y 1.3 X derivative

2, X is a vector

2.1 X scalar vector derivation of Y

2.2 Y vector derivation of the vector X

2.3 Derivation of matrix Y vector X

3, X is a matrix

4, commonly used formula

 

Matrix guide (Matrix Derivative) also called matrix differential (Matrix Differential)

 

Layout Conventions

In fact, all the rules of derivation can be derived from the most basic rules of derivation. Different literature, the same formula derivation result sometimes is not the same, look closely will find a difference of just a transposition, so we have to talk about the derivation of the two factions (layout).

Layout (Layout): There are two guides matrix layout, the layout are the denominator (denominator layout) and the molecular structure (numerator layout). These two different layouts of derivation rules are not the same. 

 

1, X is a scalar

 

1.1 Y scalar scalar derivative X

This situation is what we usually general derivation,

 

1.2 Y scalar vector derivation X

 

Scalar matrix Y 1.3 X derivative

 

2, X is a vector

 

2.1 X scalar vector derivation of Y

 

2.2 Y vector derivation of the vector X

 

2.3 Derivation of matrix Y vector X

 

3, X is a matrix

 

4, commonly used formula