LDA and support vector for classification

Question

I'm using LDA and support vector for classification. And my question is how to preprocess input data? For example: we determine, which eigenvetors of the product of the scatter matrices are responsible for the most variance, and construct a matrix W from them. Then we use this transformation matrix W to project our data on a new space, which we consequently use with support vectors. In the end, when he have a trained model from all of this, do we also need to project our input data onto the new space (multiply it by matrix W)? For example, I'm doing image classification, so I must first resize the image so that it has the same size as every other in the training dataset and then also multiply it by matrix W. And only than I can predict. Sorry in advance if I missed some of the details, I'll add them if needed.