Linear Algebra

Very useful in calculating the partition function

Diagnolizing a matrix is a transformation using its eigen space.

Canonical decomposition

Decomposing a matrix into two

$$\mathbf{A}\ast \mathbf{B}={({\mathbf{A}}_{ij}\otimes {\mathbf{B}}_{ij})}_{ij}$$

Given a matrix $\mathbf{X}\to X_m^{\phantom{m}n}$, we can decompose it into three matrices $$ …

Tucker decomposition of a generalization of SVD to higher ranks

To find the eigenvectors $\mathbf{x}$ of a matrix $\mathbf{A}$, we construct the eigen equation $$ …

Eigenstates of a very special matrix