Abstract
The matrix method given by Fujimaki and Misaki is proved to be a powerful means for the calculations of electromagnetic cascade showers at extremely high energies. The method is essentially simple and has wide applications for the calculation of cascade showers. This method is used for the calculation of the cascade showers with the LPM effect in water, for the detection of extremely high energy neutrinos. The characteristics of LPM showers in water are extracted referring to cascade showers in the absence of the LPM effect.
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