This letter investigates the variance of state dimensions of linear discrete dimension-unbounded systems, which are a class of cross-dimensional systems. First, the dimensional relationship of states, initial values and system matrices of some special cases is discussed. Then, for the general case, to directly calculate the transition time and state dimensions after the transition time, an algorithm is established on the basis of the iterative time, dimensions of initial values and system matrices. Finally, there is an illustrative example to show the effectiveness of these obtained results.

中文翻译：

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关于线性离散维数无界系统的维数

这封信研究了线性离散维无界系统的状态维方差，这是一类跨维系统。首先讨论了一些特殊情况下状态、初值和系统矩阵的维数关系。然后，对于一般情况，为了直接计算转移时间和转移时间后的状态维数，根据迭代时间、初始值维数和系统矩阵建立算法。最后，有一个说明性的例子来展示这些所得结果的有效性。