Vision Transformers (ViTs) are widely used in a variety of applications, while they usually have a fixed architecture that may not match the varying computational resources of different deployment environments. Thus, it is necessary to adapt ViT architectures to devices with diverse computational overheads to achieve an accuracy-efficient trade-off. This concept is consistent with the motivation behind Learngene. To achieve this, inspired by polynomial decomposition in calculus, where a function can be approximated by linearly combining several basic components, we propose to linearly decompose the ViT model into a set of components called learngenes during element-wise training. These learngenes can then be recomposed into differently scaled, pre-initialized models to satisfy different computational resource constraints. Such a decomposition-recomposition strategy provides an economical and flexible approach to generating different scales of ViT models for different deployment scenarios. Compared to model compression or training from scratch, which require to repeatedly train on large datasets for diverse-scale models, such strategy reduces computational costs since it only requires to train on large datasets once. Extensive experiments are used to validate the effectiveness of our method: ViTs can be decomposed and the decomposed learngenes can be recomposed into diverse-scale ViTs, which can achieve comparable or better performance compared to traditional model compression and pre-training methods. The code for our experiments is available in the supplemental material.