Different principles
The basic principle of principal component analysis (PCA): using the idea of dimensionality reduction (linear transformation), multiple indicators are transformed into several unrelated comprehensive indicators (principal components) on the premise of losing little information, that is, each principal component is a linear combination of the original variables, and the principal components are irrelevant, which makes the principal components have some superior performance than the original variables (the principal components must retain more than 90% information of the original variables).
The basic principle of factor analysis (FA): Based on the idea of dimensionality reduction, starting from studying the internal correlation of the correlation matrix of the original variables, some variables with complex relationships are represented as several common factors and a special factor that only works on one variable. It is to extract several common factors that explain variables from the data (factor analysis is the generalization of principal component, which is more inclined to describe the correlation between original variables than principal component analysis).
Linearity means different directions.
In principal component analysis, principal component is expressed as a linear combination of variables;
Factor analysis is a linear combination that represents variables as common factors.
Assuming different conditions
Principal component analysis: no hypothesis is needed;
Factor analysis: Some assumptions are needed. The assumptions of factor analysis include: there is no correlation between the same factors, between specific factors and between the same factors and specific factors.