在這篇論文中，我們主要探討在二維Hilbert空間上線性算子的三角性質。若A是一個正規矩陣，則我們發現它滿足|cos|^{2}A+|sin|^{2}A=1 和 cos^{2}A+sin^{2}A=1 這兩個等式。若A是一個非正規矩陣，我們做出一些結論，並且推測所有2 × 2的矩陣都會滿足|cos|^{2}A+|sin|^{2}A=1 的等式。

In this thesis, we study the trigonometry of linear operators on 2-dimensional Hilbert spaces. If A is a normal matrix, then we have |cos|^{2}A+|sin|^{2}A=1
and cos^{2}A+sin^{2}A=1. If A is a nonnormal matrix,
then we get some conclusions and we conjecture that
the equality |cos|^{2}A+|sin|^{2}A=1 is hold for every
two-by-two matrices.

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