Rico's Nerd Cluster

「离开世界之前一切都是过程」

Math - Null Space Pseudo Inverse

Column, Row Spaces, Projection Matrix, Full Rank Factorization

A very nice reference article in Mandarin Column, Row, Left Null and Right Null Spaces Given the linear system $A\mathbf{x}=\mathbf{b}$ with $A\in\mathbb{R}^{m\times n}$: $\textbf{Row space}$...

Posted by Rico's Nerd Cluster on January 11, 2017

Math - Matrix Derivatives

Jacobian and Hessian, Vector-Vector Derivative

Jacobian and Hessian Jacobian Suppose we have a vector-valued function \[\begin{gather*} \begin{aligned} & f = [f_0(x), ... f_m(x)] \\ & x = [x_0, ... x_n] \end{aligned} \end{gather*}\] ...

Posted by Rico's Nerd Cluster on January 10, 2017

Math - Different Types Of Convolutions

Transpose Convolution (U-Net), Dilated Convolution (DeepLab)

Transpose Convolution Definition Transpose Convolution (a.k.a upsampling convolution) was designed specifically for upsampling, which is then used in the decoder part of an encoder-decoder networ...

Posted by Rico's Nerd Cluster on January 7, 2017

Math - Gram Schmidt Orthogonolization And QR Decomposition

Gram Matrix; Super useful in finding forming an orthogonal vector basis, e.g., Singular Value Decomposition

Background Knowledge Glossary Inner product: $<a,b> = \vec{a}^T \cdot \vec{b}$, which is a.k.a “dot product” Outer product: $a \otimes b = \vec{a} \cdot \vec{b}^T$, which results in a ...

Posted by Rico's Nerd Cluster on January 5, 2017

Math - Various Useful Forms Of Matrix Multiplication

Inner & outer Product, Correlation Matrix, Matrix Inverse, Nilpotentency

Glossary Inner product: $<a,b> = \vec{a}^T \cdot \vec{b}$, which is a.k.a “dot product” Outer product: $a \otimes b = \vec{a} \cdot \vec{b}^T$, which results in a matrix. Hadamard (Sc...

Posted by Rico's Nerd Cluster on January 3, 2017