But then I have computed 30x30 elements for my eigenvector matrix and 3 parameters for my model, I have fitted 900+3 parameters to the data.

The possible solutions for the 900+3 parameters are strongly limited. You have effectively only fitted 3 parameters.

But then I have computed 30x30 elements for my eigenvector matrix and 3 parameters for my model, I have fitted 900+3 parameters to the data.

The possible solutions for the parameters relating to the features are strongly limited. You are effectively only fitting 3 parameters. Because the potential solutions $\hat{Y} = \beta_1 X_1 + \beta_2 X_2 + \dots + \beta_{30} X_{30}$ lie in a 3d space.