## Skew-symmetric matrix representation of cross product

We can define Note that we have and Triple product expansion We will show the above with the triple product expansion: Proof: (1)   Similarly for the and components. Proof of Note that for any     thus Proof of For any (2)   Thus,

## Rodrigues’ rotation formula

The rotation matrix for rotating an object along normal direction with angle is given by where such that We can easily validate that the equation is correct, note that as desired. And for any vector perpendicular to as desired as well. Compute and from  Note that  Thus, . Moreover, since , we can compute as…

## ARIMA

It is ARMA after applying lap-1 and lap-M difference to data.

## Weiszfeld’s algorithm

Came across Weiszfeld’s algorithm while reading the quaternion equivariant capsule paper.  Weiszfeld’s algorithm is just a form of iteratively reweighted least square. And the algorithm is well illustrated with this tweet.

## Jordan normal form

Any square matrix can be decomposed into Jordan normal form. The Jordan block can be decomposed into different numbers of Jordan boxes depending on the geometric multiplicity of the corresponding eigenvalues (only one box if the corresponding geometric multiplicity is one). This video series gives an excellent description to compute the Jordan normal form.

## Robust PCA

Came across of this video explaining robust PCA. It came with a book and it looks okay. As PCA can be considered as decomposition of data matrix with the highest singular value. So what PCA is doing is simply low-rank matrix approximation of the data matrix. So robust PCA is a simple idea that tries…