Condition Number

Definition

Consider a matrix $X$ with singular values $d_1\ge d_2\ge \cdots \ge d_p\ge 0$ $\kappa (X)=\frac{d_1}{d_p}$

$\kappa (X)$ is the conditional number of $X$

Facts

In linear regression, if the conditional value of the matrix $X^{⊺}X$ is large, where $X$ is a design matrix, the model has a Multicollinearity problem.