# Can PCA be used for detecting multicollinearity?

The definition of multicollinearity is:

Given a set of $N \times 1$ predictors $X = (x_1, x_2, \cdots, x_m)$, if $$x_j = \sum_{i \neq j}a_ix_i$$ then we say there is multicollinearity among the predictors.

I tend to interpret $x_j = \sum_{i \neq j}a_ix_i$ in such a way:

The variation along the $jth$ direction is explained by those directions whose $a_i$ is non-zero. If the sum can be interpreted in such a way, then by analyzing the eigenvalues of $X^TX$, we can determine whether there is multicollinearity.

Am I right?